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Will Jagy
Will Jagy
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Got a correct program going to find $m(6).$ Today is Monday, 7 October, 2013. I call it joseph.cc I started it going at 12:53 PDT, lunchtime, and put timestamps into the file that keeps the successes (of smaller size as we continue) called joseph.txt. I switched to log 10 for the output. Anyway, readable or not, here is output for the first 17 minutesfour and a half hours, followed by the program in its entirety:

jagy@phobeusjunior     116.814  
651907611648300222725782474725592418809035465656889971919224893561886421964804482955701436492603438100109520590000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^3 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^2 71^2 73^2 79^2 83^2 89^2 97^2 101^2 
17283248640000 
1296
Mon Oct  7 12:~$ tail -45 joseph.txt
     116.814  651907611648300222725782474725592418809035465656889971919224893561886421964804482955701436492603438100109520590000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^3 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^2 71^2 73^2 79^2 83^2 89^2 97^2 101^2 17283248640000 1296
Mon Oct  7 12:58:36 PDT 2013
     116.094  124169835254646341805332354513462020365253985861321166105191056581780738935164700557095176071476176867808332370000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^2 73^2 79^2 83^2 89^2 97^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     115.463  29046424422943628261615103866949719080021683800698043001118664633489149367233234767368103149465306120315244930000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 89^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.996  9904607040319497529935916619698420809889984591047268545135906220812295472907078286410964096289078630346102330000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 83^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.668  4656847467498164102113867605051993758634585584323138745492117905241838443423722829102208260688100694395561830000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^4 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^3 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.533  3413990801383729063446996805975279442431534859039247321555545609617270301842462008385267520786794596391048230000000 = 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 15122842560000 1296
Mon Oct  7 12:59:31 PDT 2013
     114.127  1338538126656619567480089762365979064306514102811004066703662170355094656013425734453274433683427522841083070000000 = 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 15122842560000 1296
Mon Oct  7 12:59:31 PDT 2013
     114.077  1193767539331957140297096557815901213255897692075957159953947066206770846878821925647640682243543917983250820000000 = 2^8 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 15122842560000 1296
Mon Oct  7 13:04:22 PDT 2013
jagy@phobeusjunior:~$58:36 PDT 2013

     116.094  
124169835254646341805332354513462020365253985861321166105191056581780738935164700557095176071476176867808332370000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^2 73^2 79^2 83^2 89^2 97^2 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     115.463  
29046424422943628261615103866949719080021683800698043001118664633489149367233234767368103149465306120315244930000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 89^2 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     114.996  
9904607040319497529935916619698420809889984591047268545135906220812295472907078286410964096289078630346102330000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 83^2 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     114.668  
4656847467498164102113867605051993758634585584323138745492117905241838443423722829102208260688100694395561830000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^4 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^3 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     114.533  
3413990801383729063446996805975279442431534859039247321555545609617270301842462008385267520786794596391048230000000 
= 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 
15122842560000 
1296
Mon Oct  7 12:59:31 PDT 2013

     114.127  
1338538126656619567480089762365979064306514102811004066703662170355094656013425734453274433683427522841083070000000 
= 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 
15122842560000 
1296
Mon Oct  7 12:59:31 PDT 2013

     114.077  
1193767539331957140297096557815901213255897692075957159953947066206770846878821925647640682243543917983250820000000 
= 2^8 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 
15122842560000 
1296
Mon Oct  7 13:04:22 PDT 2013

     113.751  
563595000697524028412669373627780658655374359078317501769963019096881960426705572401378708919337904354140240000000 
= 2^10 3^7 5^7 7^7 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 
17283248640000 
1296
Mon Oct  7 13:43:05 PDT 2013

     113.681  
479713034655167619889199144750191682431953221592392423757550900001381572388373236190584839617015121107059760000000 
= 2^10 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 
15122842560000 
1296
Mon Oct  7 13:43:38 PDT 2013

     113.317  
207611745970775154834277662228852384914069163839296897383295141949003625544142943590894031694529377040565360000000 
= 2^10 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 
15122842560000 
1296
Mon Oct  7 13:43:38 PDT 2013

     113.183  
152423056883707418625917905897515055243775047382212678813659537530460441258763728955857663845404589668440480000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^4 43^4 47^3 53^3 59^3 61^3 67^3 71^3 
15490911744000 
1296
Mon Oct  7 15:20:11 PDT 2013

     113.078  
119566635396053760260655511704533254626509877044047829323668660744724525901853491905891882920404646652772640000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^3 31^3 37^3 41^3 43^3 47^3 53^2 59^2 61^2 67^2 71^2 73^2 79^2 83^2 89^2 
9681819840000 
1296
Mon Oct  7 15:20:11 PDT 2013

     112.366  
23200848201456208751499497726280471198200439466822562008645212923196767619132535924675650050329749009634080000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^3 37^3 41^3 43^3 47^3 53^3 59^2 61^2 67^2 71^2 73^2 79^2 83^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013

      111.79  
6159725847069735201987600717283637947671447784122291466658745019092304830221136334189543321534781672030880000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^2 67^2 71^2 73^2 79^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013

     111.348  
2227607953346641940536134404568045320925245577433746489384519709676547348471255360721967517497837243033760000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^2 71^2 73^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013

      111.06  
1148290307345322839304327492840761962203349521713361157128781317785977775614662877820087215343696548435680000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^4 43^3 47^3 53^3 59^3 61^3 67^3 71^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013

Got a correct program going to find $m(6).$ Today is Monday, 7 October, 2013. I call it joseph.cc I started it going at 12:53 PDT, lunchtime, and put timestamps into the file that keeps the successes (of smaller size as we continue) called joseph.txt. I switched to log 10 for the output. Anyway, readable or not, here is output for the first 17 minutes, followed by the program in its entirety:

jagy@phobeusjunior:~$ tail -45 joseph.txt
     116.814  651907611648300222725782474725592418809035465656889971919224893561886421964804482955701436492603438100109520590000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^3 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^2 71^2 73^2 79^2 83^2 89^2 97^2 101^2 17283248640000 1296
Mon Oct  7 12:58:36 PDT 2013
     116.094  124169835254646341805332354513462020365253985861321166105191056581780738935164700557095176071476176867808332370000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^2 73^2 79^2 83^2 89^2 97^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     115.463  29046424422943628261615103866949719080021683800698043001118664633489149367233234767368103149465306120315244930000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 89^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.996  9904607040319497529935916619698420809889984591047268545135906220812295472907078286410964096289078630346102330000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 83^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.668  4656847467498164102113867605051993758634585584323138745492117905241838443423722829102208260688100694395561830000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^4 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^3 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.533  3413990801383729063446996805975279442431534859039247321555545609617270301842462008385267520786794596391048230000000 = 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 15122842560000 1296
Mon Oct  7 12:59:31 PDT 2013
     114.127  1338538126656619567480089762365979064306514102811004066703662170355094656013425734453274433683427522841083070000000 = 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 15122842560000 1296
Mon Oct  7 12:59:31 PDT 2013
     114.077  1193767539331957140297096557815901213255897692075957159953947066206770846878821925647640682243543917983250820000000 = 2^8 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 15122842560000 1296
Mon Oct  7 13:04:22 PDT 2013
jagy@phobeusjunior:~$

Got a correct program going to find $m(6).$ Today is Monday, 7 October, 2013. I call it joseph.cc I started it going at 12:53 PDT, lunchtime, and put timestamps into the file that keeps the successes (of smaller size as we continue) called joseph.txt. I switched to log 10 for the output. Anyway, readable or not, here is output for the first four and a half hours, followed by the program in its entirety:

     116.814  
651907611648300222725782474725592418809035465656889971919224893561886421964804482955701436492603438100109520590000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^3 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^2 71^2 73^2 79^2 83^2 89^2 97^2 101^2 
17283248640000 
1296
Mon Oct  7 12:58:36 PDT 2013

     116.094  
124169835254646341805332354513462020365253985861321166105191056581780738935164700557095176071476176867808332370000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^2 73^2 79^2 83^2 89^2 97^2 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     115.463  
29046424422943628261615103866949719080021683800698043001118664633489149367233234767368103149465306120315244930000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 89^2 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     114.996  
9904607040319497529935916619698420809889984591047268545135906220812295472907078286410964096289078630346102330000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 83^2 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     114.668  
4656847467498164102113867605051993758634585584323138745492117905241838443423722829102208260688100694395561830000000 
= 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^4 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^3 
17283248640000 
1296
Mon Oct  7 12:58:37 PDT 2013

     114.533  
3413990801383729063446996805975279442431534859039247321555545609617270301842462008385267520786794596391048230000000 
= 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 
15122842560000 
1296
Mon Oct  7 12:59:31 PDT 2013

     114.127  
1338538126656619567480089762365979064306514102811004066703662170355094656013425734453274433683427522841083070000000 
= 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 
15122842560000 
1296
Mon Oct  7 12:59:31 PDT 2013

     114.077  
1193767539331957140297096557815901213255897692075957159953947066206770846878821925647640682243543917983250820000000 
= 2^8 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 
15122842560000 
1296
Mon Oct  7 13:04:22 PDT 2013

     113.751  
563595000697524028412669373627780658655374359078317501769963019096881960426705572401378708919337904354140240000000 
= 2^10 3^7 5^7 7^7 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 
17283248640000 
1296
Mon Oct  7 13:43:05 PDT 2013

     113.681  
479713034655167619889199144750191682431953221592392423757550900001381572388373236190584839617015121107059760000000 
= 2^10 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 
15122842560000 
1296
Mon Oct  7 13:43:38 PDT 2013

     113.317  
207611745970775154834277662228852384914069163839296897383295141949003625544142943590894031694529377040565360000000 
= 2^10 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 
15122842560000 
1296
Mon Oct  7 13:43:38 PDT 2013

     113.183  
152423056883707418625917905897515055243775047382212678813659537530460441258763728955857663845404589668440480000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^4 43^4 47^3 53^3 59^3 61^3 67^3 71^3 
15490911744000 
1296
Mon Oct  7 15:20:11 PDT 2013

     113.078  
119566635396053760260655511704533254626509877044047829323668660744724525901853491905891882920404646652772640000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^3 31^3 37^3 41^3 43^3 47^3 53^2 59^2 61^2 67^2 71^2 73^2 79^2 83^2 89^2 
9681819840000 
1296
Mon Oct  7 15:20:11 PDT 2013

     112.366  
23200848201456208751499497726280471198200439466822562008645212923196767619132535924675650050329749009634080000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^3 37^3 41^3 43^3 47^3 53^3 59^2 61^2 67^2 71^2 73^2 79^2 83^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013

      111.79  
6159725847069735201987600717283637947671447784122291466658745019092304830221136334189543321534781672030880000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^2 67^2 71^2 73^2 79^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013

     111.348  
2227607953346641940536134404568045320925245577433746489384519709676547348471255360721967517497837243033760000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^2 71^2 73^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013

      111.06  
1148290307345322839304327492840761962203349521713361157128781317785977775614662877820087215343696548435680000000 
= 2^11 3^11 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^4 43^3 47^3 53^3 59^3 61^3 67^3 71^2 
9681819840000 
1296
Mon Oct  7 15:20:12 PDT 2013
added 54 characters in body
Source Link
Will Jagy
Will Jagy
  • 25.7k
  • 2
  • 65
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    #include <iostream>
    #include <stdlib.h>
    #include <fstream>
    #include <sstream>
    #include <strstream>
    #include <list>
    #include <set>
    #include <math.h>
    #include <iomanip>
    #include <string>
    #include <algorithm>
    #include <iterator>
    
    
    #include <gmp.h>
    #include <gmpxx.h>
    
    using namespace std;
    
    
    
    
    // const double my_pi = 4 * atan(1.0);
    const double E_TO_THE_GAMMA  = 1.7810724179901979852365 ;
    const double GAMMA  = 0.57721566490153286060 ;
    const int BOUND = 1875;
 
//  joseph.cc   



 
//  g++  -o// joseph joseph.cc  -lgmp -lgmpxx



string stringify(int x)
 { 
   ostringstream o;
   o << x  ;
   return o.str();
 }





string mp_Factored( mpz_class  i)
{
//  stringg++ fac;
 -o facjoseph =joseph.cc " =-lgmp ";-lgmpxx
  int p = 2;
   mpz_class  
 temp = i; 
  if (temp <string 0stringify(int x)
     {
    temp *= -1; ostringstream o;
    fac += " -1o *<< ";
x  }
;
  if ( 1 == temp return o.str();
 fac += " 1 ";}
  if ( temp 
 > 1)
  {
    int 
 primefac = 0;
  
   while( temp 
 > 1 && pstring *mp_Factored( pmpz_class <= tempi)
    {
      ifstring (tempfac;
 %     fac = " = ";
      int p === 2;
       mpz_class  temp = i;
      if (temp < 0 )
      {
        ++primefac;
  temp *= -1;
    if (primefac > 1) fac += " ";
    -1 * ";
   fac += stringify( p) ;}
     
    temp /= p;
  if ( 1 == temp) fac int+= exponent" =1 1;";
        whileif (temp % ptemp ==> 01)
        {
         int tempprimefac /= p;
          ++exponent;0;
        } // while p is fac
   ( temp > 1 && ifp (* exponentp ><= 1temp)
        {
          if (temp % p == 0)
          {
            ++primefac;
            if (primefac > 1) fac += "^"" ;";
             fac += stringify( exponentp) ;
        }    temp /= p;
      }  // if   int exponent = 1;
            while (temp % p is== factor0)
      ++p;      {
              temp /= p;
              ++exponent;
            } // while p is fac
            if (temp exponent > 1)
 && primefac >= 1)        {
              fac += ""^" ";;
    if (temp > 1 )      fac += stringify( temp.get_ui()exponent)  ;
  } // temp > 1
  return fac;   }
          }  // mp_Factored


if p is factor
//  g++  -o joseph joseph.cc  -lgmp -lgmpxx

 ++p;
 mpz_class  intpow(int n, int k)
{
  } // mpz_classwhile blobp
 = 1;
   for(int j = 1;if j(temp <=> k;1 ++j&& primefac >= 1) blobfac *=+= n;
" ";
   return ( blob );

}


 mpz_class orourkeif (temp mpz_class> i1 )
{
 fac mpz_class+= joestringify( =temp.get_ui()) 1;
 ;
  int p = 2;
 } mpz_class// temp => i;1
  if (temp < 0 )
 return {fac;
    temp} *=// -1;mp_Factored
  
   }
    
    
  if ( temp// > 1)
g++  {-o joseph joseph.cc  -lgmp -lgmpxx
    
    while( 
 temp > 1 && pmpz_class * pintpow(int <=n, tempint k)
    {
      if  mpz_class blob = 1;
       for(tempint %j = 1; j <= k; ++j) blob *= n;
    
       return ( blob );
    
    }
    
    
     mpz_class orourke( mpz_class i)
    {
      mpz_class joe = 1;
     
      int p === 2;
      mpz_class temp = i;
      if (temp < 0 )
      {
   
        temp /= p;
        int exponent =*= -1;
        
 while (temp % p == 0)}
     
    {
        if ( temp /=> p;1)
          ++exponent;{
        
 } // while p is fac
   while( temp > 1 && ifp (* exponentp ><= 1temp)
        {
        
          joe *= exponent ;
        }
      }  // if p is factor
      ++p;
    } // while p
   
  } // temp > 1
  return joe;
} // orourke



//  g++  -o joseph joseph.cc  -lgmp -lgmpxx


int main()
{

   ofstream erasefile("joseph.txt");
  erasefile.close();



    double luge = 0.0;
  double luge_boundtemp =% 270.0;p == //270.0)
     // product of exponents
   for( int e2 = 2; e2 * log(2.0) <  luge_bound  ; ++e2){
      mpz_class  p2 =   intpow(2, e2) ;
      double luge2 =   e2 * log(2.0) ; 

temp //   cerr << "2^" << e2 << endl;

    for( int e3 = 0; e3 <= e2 && luge2 + e3 * log(3.0) <  luge_bound  ; ++e3){
      mpz_class  p3 = p2 *  intpow(3, e3) ;
      double luge3 = luge2 + e3 * log(3.0)  ; 
p;
 //   cerr << "2^" << e2 << "  3^" << e3 << endl;

    for( int e5exponent = 0; e5 <= e3 && luge3 + e5 * log(5.0) <  luge_bound  ; ++e5){1;
      mpz_class  p5 = p3 * while intpow(5, e5) ;
      double luge5 = luge3temp +% e5p *== log(5.0)  ; 

 //   cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5 << endl;

    for( int e7 = 0; e7 <= e5 && luge5 + e7 * log(7.0) <  luge_bound  ; ++e7){
      mpz_class  p7 = p5 *  intpow(7, e7) ;
      double luge7temp /= luge5 + e7 * log(7.0)  ; 
p;
    cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5  << "  7^" << e7  << endl;
       system("date");++exponent;
         cout << endl;



    for( int e11 = 0; e11 <= e7 && luge7 + e11 * log(11.0) <} // luge_boundwhile p ;is ++e11){fac
      mpz_class  p11 = p7 * if intpow(11, e11) ;
      double luge11 = luge7 + e11exponent *> log(11.01)  ; 

    for( int e13 = 0; e13 <= e11 && luge11 + e13 * log(13.0) <  luge_bound  ; ++e13){
      mpz_class  p13 = p11 *  intpow(13, e13) ;
      double luge13 = luge11 + e13 * log(13.0)  ; 

    for( int e17 = 0; e17 <= e13 && luge13 + e17 * log(17.0) < joe luge_bound*= exponent ; ++e17){
      mpz_class  p17 = p13 *  intpow(17, e17) ;}
      double luge17 = luge13 +} e17 *// log(17.0)if p ;is 
 factor
    for( int e19 = 0; e19 <= e17 && luge17 + e19 * log(19.0) <  luge_bound  ; ++e19){++p;
      mpz_class  p19 = p17 * } intpow(19,// e19)while ;p
      double luge19 = luge17 + e19 * log(19.0)  ; 
 
    for( int e23 = 0; e23 <= e19 && luge19 + e23 * log(23.0) < } luge_bound// temp ;> ++e23){1
      mpz_class  p23 = p19 *  intpow(23, e23)return ;joe;
      double luge23 = luge19 + e23 * log(23.0) } ;// orourke
    
    for( int e29 = 0; e29 <= e23 && luge23 + e29 * log(29.0) <  luge_bound  ; ++e29){
      mpz_class  p29 = p23 *  intpow(29, e29) ;
      double luge29 = luge23 + e29 * log(29.0)  ; 
    
    for( int e31 = 0; e31 <= e29 && luge29 + e31 * log(31.0) <  luge_bound  ; ++e31){
      mpz_class  p31 = p29 *  intpow(31, e31) ;
      double luge31 = luge29 + e31 * log(31.0)  ; 

    for( int e37 = 0; e37 <= e31 && luge31 + e37 * log(37.0) <  luge_bound  ; ++e37){
      mpz_class  p37 = p31 *  intpow(37, e37) ;
      double luge37 = luge31 + e37 * log(37.0)  ; 

    for( int e41 = 0; e41 <= e37 && luge37 + e41 * log(41.0) <  luge_bound  ; ++e41){
      mpz_class  p41 = p37 *  intpow(41, e41) ;
      double luge41 = luge37 + e41 * log(41.0)  ; 

    for( int e43 = 0; e43 <= e41 && luge41 + e43 * log(43.0) <  luge_bound  ; ++e43){
      mpz_class  p43 = p41 *  intpow(43, e43) ;
      double luge43 = luge41 + e43 * log(43.0)  ; 

    for( int e47 = 0; e47 <= e43 && luge43 + e47 * log(47.0) <  luge_bound  ; ++e47){
      mpz_class  p47 = p43 *  intpow(47, e47) ;
      double luge47 = luge43 + e47 * log(47.0)  ; 

    for( int e53 = 0; e53 <= e47 && luge47 + e53 * log(53.0) <  luge_bound  ; ++e53){
      mpz_class  p53 = p47 *  intpow(53, e53) ;
      double luge53 = luge47 + e53 * log(53.0)  ; 

    for( int e59 = 0; e59 <= e53 && luge53 + e59 * log(59.0) <  luge_bound  ; ++e59){
      mpz_class  p59 = p53 *  intpow(59, e59) ;
      double luge59 = luge53 + e59 * log(59.0)  ; 

    for( int e61 = 0; e61 <= e59 && luge59 + e61 * log(61.0) <  luge_bound  ; ++e61){
      mpz_class  p61 = p59 *  intpow(61, e61) ;
      double luge61 = luge59 + e61 * log(61.0)  ; 

    for( int e67 = 0; e67 <= e61 && luge61 + e67 * log(67.0) <  luge_bound  ; ++e67){
      mpz_class  p67 = p61 *  intpow(67, e67) ;
      double luge67 = luge61 + e67 * log(67.0)  ; 

    for( int e71 = 0; e71 <= e67 && luge67 + e71 * log(71.0) <  luge_bound  ; ++e71){
      mpz_class  p71 = p67 *  intpow(71, e71) ;
      double luge71 = luge67 + e71 * log(71.0)  ; 

    for( int e73 = 0; e73 <= e71 && luge71 + e73 * log(73.0) <  luge_bound  ; ++e73){
      mpz_class  p73 = p71 *  intpow(73, e73) ;
      double luge73 = luge71 + e73 * log(73.0)  ; 

    for( int e79 = 0; e79 <= e73 && luge73 + e79 * log(79.0) <  luge_bound  ; ++e79){
      mpz_class  p79 = p73 *  intpow(79, e79) ;
      double luge79 = luge73 + e79 * log(79.0)  ; 

    for( int e83 = 0; e83 <= e79 && luge79 + e83 * log(83.0) <  luge_bound  ; ++e83){
      mpz_class  p83 = p79 *  intpow(83, e83) ;
      double luge83 = luge79 + e83 * log(83.0)  ; 

    for( int e89 = 0; e89 <= e83 && luge83 + e89 * log(89.0) <  luge_bound  ; ++e89){
      mpz_class  p89 = p83 *  intpow(89, e89) ;
      double luge89 = luge83 + e89 * log(89.0)  ; 

    for( int e97 = 0; e97 <= e89 && luge89 + e97 * log(97.0) <  luge_bound  ; ++e97){
      mpz_class  p97 = p89 *  intpow(97, e97) ;
      double luge97 = luge89 + e97 * log(97.0)  ; 

    for( int e101 = 0; e101 <= e97 && luge97 + e101 * log(101.0) <  luge_bound  ; ++e101){
      mpz_class  p101 = p97 *  intpow(101, e101) ;
      double luge101 = luge97 + e101 * log(101.0)  ; 

    for( int e103 = 0; e103 <= e101 && luge101 + e103 * log(103.0) <  luge_bound  ; ++e103){
      mpz_class  p103 = p101 *  intpow(103, e103) ;
      double luge103 = luge101 + e103 * log(103.0)  ; 

    for( int e107 = 0; e107 <= e103 && luge103 + e107 * log(107.0) <  luge_bound  ; ++e107){
      mpz_class  p107 = p103 *  intpow(107, e107) ;
      double luge107 = luge103 + e107 * log(107.0)  ; 

    for( int e109 = 0; e109 <= e107 && luge107 + e109 * log(109.0) <  luge_bound  ; ++e109){
      mpz_class  p109 = p107 *  intpow(109, e109) ;
      double luge109 = luge107 + e109 * log(109.0)  ; 

    for( int e113 = 0; e113 <= e109 && luge109 + e113 * log(113.0) <  luge_bound  ; ++e113){
      mpz_class  p113 = p109 *  intpow(113, e113) ;
      double luge113 = luge109 + e113 * log(113.0)  ; 

    for( int e127 = 0; e127 <= e113 && luge113 + e127 * log(127.0) <  luge_bound  ; ++e127){
      mpz_class  p127 = p113 *  intpow(127, e127) ;
      double luge127 = luge113 + e127 * log(127.0)  ; 

    for( int e131 = 0; e131 <= e127 && luge127 + e131 * log(131.0) <  luge_bound  ; ++e131){
      mpz_class  p131 = p127 *  intpow(131, e131) ;
      double luge131 = luge127 + e131 * log(131.0)  ; 

    for( int e137 = 0; e137 <= e131 && luge131 + e137 * log(137.0) <  luge_bound  ; ++e137){
      mpz_class  p137 = p131 *  intpow(137, e137) ;
      double luge137 = luge131 + e137 * log(137.0)  ; 

    for( int e139 = 0; e139 <= e137 && luge137 + e139 * log(139.0) <  luge_bound  ; ++e139){
      mpz_class  p139 = p137 *  intpow(139, e139) ;
      double luge139 = luge137 + e139 * log(139.0)  ; 

    for( int e149 = 0; e149 <= e139 && luge139 + e149 * log(149.0) <  luge_bound  ; ++e149){
      mpz_class  p149 = p139 *  intpow(149, e149) ;
      double luge149 = luge139 + e149 * log(149.0)  ; 


//  g++  -o joseph joseph.cc  -lgmp -lgmpxx
 
     mpz_class p = p149;
     double luge = luge149;

    if (   orourke(orourke(orourke(orourke(orourke(p))))) != 1 &&   int orourke(orourke(orourke(orourke(orourke(orourkemain(p)))))) == 1  && luge < luge_bound  ) 
    {
     
      cout <<ofstream erasefile("joseph.txt");
  setw    erasefile.close(12);
 <<   
    
    
  //      double luge = 0.0; // declared later although compile did not complain
      double luge_bound = 270.0;  //270.0
         // product of exponents
       for( int e2 = 2; e2 * log(102.0) <<< " luge_bound " ; <<++e2){
 p << mp_Factored       mpz_class  p2 =   intpow(p2, e2) <<;
 " " << orourke      double luge2 =   e2 * log(p2.0) ; 
    
     //   cerr << "2^" << e2 << endl;
     
     luge_bound   for( int e3 = luge;0; e3 <= e2 && luge2 + e3 * log(3.0) <  luge_bound  ; ++e3){
          mpz_class  p3 = p2 *  intpow(3, e3) ;
          double ofstreamluge3 outfile= luge2 + e3 * log("joseph3.txt",ios::app0)  ; 
     
     outfile//   cerr << "2^" setw<< e2 << "  3^" << e3 << endl;
    
        for(12 int e5 = 0; e5 <= e3 && luge3 + e5 * log(5.0) <<< luge /luge_bound  ; ++e5){
          mpz_class  p5 = p3 *  intpow(5, e5) ;
          double luge5 = luge3 + e5 * log(105.0)  ; 
    
     //   cerr << "2^" << e2 << "  3^" << e3  << "  5^" << pe5 << mp_Factoredendl;
    
        for(p int e7 = 0; e7 <= e5 && luge5 + e7 * log(7.0) <  luge_bound  ; ++e7){
          mpz_class  p7 = p5 *  intpow(7, e7) ;
          double luge7 = luge5 + e7 * log(7.0)  ; 
    
        cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5  orourke<< "  7^" << e7  << endl;
           system(p"date");
  << " "         cout << endl;
   orourke 
    
    
        for(orourke int e11 = 0; e11 <= e7 && luge7 + e11 * log(p11.0) <  luge_bound  ; ++e11){
 << endl;        mpz_class  p11 = p7 *  intpow(11, e11) ;
          double luge11 = luge7 + e11 * log(11.0)  ; 
    
        for( int e13 = 0; e13 <= e11 && luge11 + e13 * log(13.0) <  luge_bound  ; ++e13){
          mpz_class  p13 = p11 *  intpow(13, e13) ;
          double luge13 = luge11 + e13 * log(13.0)  ; 
    
        for( int e17 = 0; e17 <= e13 && luge13 + e17 * log(17.0) <  luge_bound  ; ++e17){
          mpz_class  p17 = p13 *  intpow(17, e17) ;
          double luge17 = luge13 + e17 * log(17.0)  ; 
    
        for( int e19 = 0; e19 <= e17 && luge17 + e19 * log(19.0) <  luge_bound  ; ++e19){
          mpz_class  p19 = p17 *  intpow(19, e19) ;
          double luge19 = luge17 + e19 * log(19.0)  ; 
    
        for( int e23 = 0; e23 <= e19 && luge19 + e23 * log(23.0) <  luge_bound  ; ++e23){
          mpz_class  p23 = p19 *  intpow(23, e23) ;
          double luge23 = luge19 + e23 * log(23.0)  ; 
        
        outfile.close();  // close quickly save partial progress
       system("date >> joseph.txt") ;


  
    } // if

   } // 149
   } // 139
   } // 137
   } // 131
   } // 127
   } // 113
   } // 109
   } // 107
   } // 103
   } // 101
   } // 97
   } // 89
   } // 83
   } // 79
   } // 73
   } // 71
   } // 67
   } // 61
   } // 59
   } // 53
   } // 47
   } // 43
   } // 41
   } // 37
   } // 31
   } // 29
   } // 23
   } // 19
   } // 17
   } // 13
   } // 11
   } // 7
   } // 5
   } // 3
   } // 2


    return 0 ;
}
       for( int e29 = 0; e29 <= e23 && luge23 + e29 * log(29.0) <  luge_bound  ; ++e29){
          mpz_class  p29 = p23 *  intpow(29, e29) ;
          double luge29 = luge23 + e29 * log(29.0)  ; 
        
        for( int e31 = 0; e31 <= e29 && luge29 + e31 * log(31.0) <  luge_bound  ; ++e31){
          mpz_class  p31 = p29 *  intpow(31, e31) ;
          double luge31 = luge29 + e31 * log(31.0)  ; 
    
        for( int e37 = 0; e37 <= e31 && luge31 + e37 * log(37.0) <  luge_bound  ; ++e37){
          mpz_class  p37 = p31 *  intpow(37, e37) ;
          double luge37 = luge31 + e37 * log(37.0)  ; 
    
        for( int e41 = 0; e41 <= e37 && luge37 + e41 * log(41.0) <  luge_bound  ; ++e41){
          mpz_class  p41 = p37 *  intpow(41, e41) ;
          double luge41 = luge37 + e41 * log(41.0)  ; 
    
        for( int e43 = 0; e43 <= e41 && luge41 + e43 * log(43.0) <  luge_bound  ; ++e43){
          mpz_class  p43 = p41 *  intpow(43, e43) ;
          double luge43 = luge41 + e43 * log(43.0)  ; 
    
        for( int e47 = 0; e47 <= e43 && luge43 + e47 * log(47.0) <  luge_bound  ; ++e47){
          mpz_class  p47 = p43 *  intpow(47, e47) ;
          double luge47 = luge43 + e47 * log(47.0)  ; 
    
        for( int e53 = 0; e53 <= e47 && luge47 + e53 * log(53.0) <  luge_bound  ; ++e53){
          mpz_class  p53 = p47 *  intpow(53, e53) ;
          double luge53 = luge47 + e53 * log(53.0)  ; 
    
        for( int e59 = 0; e59 <= e53 && luge53 + e59 * log(59.0) <  luge_bound  ; ++e59){
          mpz_class  p59 = p53 *  intpow(59, e59) ;
          double luge59 = luge53 + e59 * log(59.0)  ; 
    
        for( int e61 = 0; e61 <= e59 && luge59 + e61 * log(61.0) <  luge_bound  ; ++e61){
          mpz_class  p61 = p59 *  intpow(61, e61) ;
          double luge61 = luge59 + e61 * log(61.0)  ; 
    
        for( int e67 = 0; e67 <= e61 && luge61 + e67 * log(67.0) <  luge_bound  ; ++e67){
          mpz_class  p67 = p61 *  intpow(67, e67) ;
          double luge67 = luge61 + e67 * log(67.0)  ; 
    
        for( int e71 = 0; e71 <= e67 && luge67 + e71 * log(71.0) <  luge_bound  ; ++e71){
          mpz_class  p71 = p67 *  intpow(71, e71) ;
          double luge71 = luge67 + e71 * log(71.0)  ; 
    
        for( int e73 = 0; e73 <= e71 && luge71 + e73 * log(73.0) <  luge_bound  ; ++e73){
          mpz_class  p73 = p71 *  intpow(73, e73) ;
          double luge73 = luge71 + e73 * log(73.0)  ; 
    
        for( int e79 = 0; e79 <= e73 && luge73 + e79 * log(79.0) <  luge_bound  ; ++e79){
          mpz_class  p79 = p73 *  intpow(79, e79) ;
          double luge79 = luge73 + e79 * log(79.0)  ; 
    
        for( int e83 = 0; e83 <= e79 && luge79 + e83 * log(83.0) <  luge_bound  ; ++e83){
          mpz_class  p83 = p79 *  intpow(83, e83) ;
          double luge83 = luge79 + e83 * log(83.0)  ; 
    
        for( int e89 = 0; e89 <= e83 && luge83 + e89 * log(89.0) <  luge_bound  ; ++e89){
          mpz_class  p89 = p83 *  intpow(89, e89) ;
          double luge89 = luge83 + e89 * log(89.0)  ; 
    
        for( int e97 = 0; e97 <= e89 && luge89 + e97 * log(97.0) <  luge_bound  ; ++e97){
          mpz_class  p97 = p89 *  intpow(97, e97) ;
          double luge97 = luge89 + e97 * log(97.0)  ; 
    
        for( int e101 = 0; e101 <= e97 && luge97 + e101 * log(101.0) <  luge_bound  ; ++e101){
          mpz_class  p101 = p97 *  intpow(101, e101) ;
          double luge101 = luge97 + e101 * log(101.0)  ; 
    
        for( int e103 = 0; e103 <= e101 && luge101 + e103 * log(103.0) <  luge_bound  ; ++e103){
          mpz_class  p103 = p101 *  intpow(103, e103) ;
          double luge103 = luge101 + e103 * log(103.0)  ; 
    
        for( int e107 = 0; e107 <= e103 && luge103 + e107 * log(107.0) <  luge_bound  ; ++e107){
          mpz_class  p107 = p103 *  intpow(107, e107) ;
          double luge107 = luge103 + e107 * log(107.0)  ; 
    
        for( int e109 = 0; e109 <= e107 && luge107 + e109 * log(109.0) <  luge_bound  ; ++e109){
          mpz_class  p109 = p107 *  intpow(109, e109) ;
          double luge109 = luge107 + e109 * log(109.0)  ; 
    
        for( int e113 = 0; e113 <= e109 && luge109 + e113 * log(113.0) <  luge_bound  ; ++e113){
          mpz_class  p113 = p109 *  intpow(113, e113) ;
          double luge113 = luge109 + e113 * log(113.0)  ; 
    
        for( int e127 = 0; e127 <= e113 && luge113 + e127 * log(127.0) <  luge_bound  ; ++e127){
          mpz_class  p127 = p113 *  intpow(127, e127) ;
          double luge127 = luge113 + e127 * log(127.0)  ; 
    
        for( int e131 = 0; e131 <= e127 && luge127 + e131 * log(131.0) <  luge_bound  ; ++e131){
          mpz_class  p131 = p127 *  intpow(131, e131) ;
          double luge131 = luge127 + e131 * log(131.0)  ; 
    
        for( int e137 = 0; e137 <= e131 && luge131 + e137 * log(137.0) <  luge_bound  ; ++e137){
          mpz_class  p137 = p131 *  intpow(137, e137) ;
          double luge137 = luge131 + e137 * log(137.0)  ; 
    
        for( int e139 = 0; e139 <= e137 && luge137 + e139 * log(139.0) <  luge_bound  ; ++e139){
          mpz_class  p139 = p137 *  intpow(139, e139) ;
          double luge139 = luge137 + e139 * log(139.0)  ; 
    
        for( int e149 = 0; e149 <= e139 && luge139 + e149 * log(149.0) <  luge_bound  ; ++e149){
          mpz_class  p149 = p139 *  intpow(149, e149) ;
          double luge149 = luge139 + e149 * log(149.0)  ; 
    
    
    //  g++  -o joseph joseph.cc  -lgmp -lgmpxx
    
         mpz_class p = p149;
         double luge = luge149;
    
        if (   orourke(orourke(orourke(orourke(orourke(p))))) != 1 &&    orourke(orourke(orourke(orourke(orourke(orourke(p)))))) == 1  && luge < luge_bound  ) 
        {
              cout <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " << orourke(p) << endl;
             luge_bound = luge;
      
               ofstream outfile("joseph.txt",ios::app);
             outfile <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " <<   orourke(p)  << " " <<    orourke(orourke(p)) << endl;
            
            outfile.close();  // close quickly save partial progress
           system("date >> joseph.txt") ;
    
    
      
        } // if
    
       } // 149
       } // 139
       } // 137
       } // 131
       } // 127
       } // 113
       } // 109
       } // 107
       } // 103
       } // 101
       } // 97
       } // 89
       } // 83
       } // 79
       } // 73
       } // 71
       } // 67
       } // 61
       } // 59
       } // 53
       } // 47
       } // 43
       } // 41
       } // 37
       } // 31
       } // 29
       } // 23
       } // 19
       } // 17
       } // 13
       } // 11
       } // 7
       } // 5
       } // 3
       } // 2
    
    
        return 0 ;
    }

#include <iostream>
#include <stdlib.h>
#include <fstream>
#include <sstream>
#include <strstream>
#include <list>
#include <set>
#include <math.h>
#include <iomanip>
#include <string>
#include <algorithm>
#include <iterator>


#include <gmp.h>
#include <gmpxx.h>

using namespace std;




// const double my_pi = 4 * atan(1.0);
const double E_TO_THE_GAMMA  = 1.7810724179901979852365 ;
const double GAMMA  = 0.57721566490153286060 ;
const int BOUND = 1875;
 
//  joseph.cc   



 
//  g++  -o joseph joseph.cc  -lgmp -lgmpxx



string stringify(int x)
 {
   ostringstream o;
   o << x  ;
   return o.str();
 }





string mp_Factored( mpz_class  i)
{
  string fac;
  fac = " = ";
  int p = 2;
   mpz_class  temp = i;
  if (temp < 0 )
  {
    temp *= -1;
    fac += " -1 * ";
  }

  if ( 1 == temp) fac += " 1 ";
  if ( temp > 1)
  {
    int primefac = 0;
    while( temp > 1 && p * p <= temp)
    {
      if (temp % p == 0)
      {
        ++primefac;
        if (primefac > 1) fac += " ";
         fac += stringify( p) ;
        temp /= p;
        int exponent = 1;
        while (temp % p == 0)
        {
          temp /= p;
          ++exponent;
        } // while p is fac
        if ( exponent > 1)
        {
          fac += "^" ;
          fac += stringify( exponent) ;
        }
      }  // if p is factor
      ++p;
    } // while p
    if (temp > 1 && primefac >= 1) fac += " ";
    if (temp > 1 ) fac += stringify( temp.get_ui())  ;
  } // temp > 1
  return fac;
} // mp_Factored



//  g++  -o joseph joseph.cc  -lgmp -lgmpxx


 mpz_class  intpow(int n, int k)
{
    mpz_class blob = 1;
   for(int j = 1; j <= k; ++j) blob *= n;

   return ( blob );

}


 mpz_class orourke( mpz_class i)
{
  mpz_class joe = 1;
 
  int p = 2;
  mpz_class temp = i;
  if (temp < 0 )
  {
    temp *= -1;
  
   }


  if ( temp > 1)
  {
   
    while( temp > 1 && p * p <= temp)
    {
      if (temp % p == 0)
      {
   
        temp /= p;
        int exponent = 1;
        while (temp % p == 0)
        {
          temp /= p;
          ++exponent;
        } // while p is fac
        if ( exponent > 1)
        {
        
          joe *= exponent ;
        }
      }  // if p is factor
      ++p;
    } // while p
   
  } // temp > 1
  return joe;
} // orourke



//  g++  -o joseph joseph.cc  -lgmp -lgmpxx


int main()
{

   ofstream erasefile("joseph.txt");
  erasefile.close();



    double luge = 0.0;
  double luge_bound = 270.0;  //270.0
     // product of exponents
   for( int e2 = 2; e2 * log(2.0) <  luge_bound  ; ++e2){
      mpz_class  p2 =   intpow(2, e2) ;
      double luge2 =   e2 * log(2.0) ; 

 //   cerr << "2^" << e2 << endl;

    for( int e3 = 0; e3 <= e2 && luge2 + e3 * log(3.0) <  luge_bound  ; ++e3){
      mpz_class  p3 = p2 *  intpow(3, e3) ;
      double luge3 = luge2 + e3 * log(3.0)  ; 

 //   cerr << "2^" << e2 << "  3^" << e3 << endl;

    for( int e5 = 0; e5 <= e3 && luge3 + e5 * log(5.0) <  luge_bound  ; ++e5){
      mpz_class  p5 = p3 *  intpow(5, e5) ;
      double luge5 = luge3 + e5 * log(5.0)  ; 

 //   cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5 << endl;

    for( int e7 = 0; e7 <= e5 && luge5 + e7 * log(7.0) <  luge_bound  ; ++e7){
      mpz_class  p7 = p5 *  intpow(7, e7) ;
      double luge7 = luge5 + e7 * log(7.0)  ; 

    cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5  << "  7^" << e7  << endl;
       system("date");
         cout << endl;



    for( int e11 = 0; e11 <= e7 && luge7 + e11 * log(11.0) <  luge_bound  ; ++e11){
      mpz_class  p11 = p7 *  intpow(11, e11) ;
      double luge11 = luge7 + e11 * log(11.0)  ; 

    for( int e13 = 0; e13 <= e11 && luge11 + e13 * log(13.0) <  luge_bound  ; ++e13){
      mpz_class  p13 = p11 *  intpow(13, e13) ;
      double luge13 = luge11 + e13 * log(13.0)  ; 

    for( int e17 = 0; e17 <= e13 && luge13 + e17 * log(17.0) <  luge_bound  ; ++e17){
      mpz_class  p17 = p13 *  intpow(17, e17) ;
      double luge17 = luge13 + e17 * log(17.0)  ; 
 
    for( int e19 = 0; e19 <= e17 && luge17 + e19 * log(19.0) <  luge_bound  ; ++e19){
      mpz_class  p19 = p17 *  intpow(19, e19) ;
      double luge19 = luge17 + e19 * log(19.0)  ; 
 
    for( int e23 = 0; e23 <= e19 && luge19 + e23 * log(23.0) <  luge_bound  ; ++e23){
      mpz_class  p23 = p19 *  intpow(23, e23) ;
      double luge23 = luge19 + e23 * log(23.0)  ; 
    
    for( int e29 = 0; e29 <= e23 && luge23 + e29 * log(29.0) <  luge_bound  ; ++e29){
      mpz_class  p29 = p23 *  intpow(29, e29) ;
      double luge29 = luge23 + e29 * log(29.0)  ; 
    
    for( int e31 = 0; e31 <= e29 && luge29 + e31 * log(31.0) <  luge_bound  ; ++e31){
      mpz_class  p31 = p29 *  intpow(31, e31) ;
      double luge31 = luge29 + e31 * log(31.0)  ; 

    for( int e37 = 0; e37 <= e31 && luge31 + e37 * log(37.0) <  luge_bound  ; ++e37){
      mpz_class  p37 = p31 *  intpow(37, e37) ;
      double luge37 = luge31 + e37 * log(37.0)  ; 

    for( int e41 = 0; e41 <= e37 && luge37 + e41 * log(41.0) <  luge_bound  ; ++e41){
      mpz_class  p41 = p37 *  intpow(41, e41) ;
      double luge41 = luge37 + e41 * log(41.0)  ; 

    for( int e43 = 0; e43 <= e41 && luge41 + e43 * log(43.0) <  luge_bound  ; ++e43){
      mpz_class  p43 = p41 *  intpow(43, e43) ;
      double luge43 = luge41 + e43 * log(43.0)  ; 

    for( int e47 = 0; e47 <= e43 && luge43 + e47 * log(47.0) <  luge_bound  ; ++e47){
      mpz_class  p47 = p43 *  intpow(47, e47) ;
      double luge47 = luge43 + e47 * log(47.0)  ; 

    for( int e53 = 0; e53 <= e47 && luge47 + e53 * log(53.0) <  luge_bound  ; ++e53){
      mpz_class  p53 = p47 *  intpow(53, e53) ;
      double luge53 = luge47 + e53 * log(53.0)  ; 

    for( int e59 = 0; e59 <= e53 && luge53 + e59 * log(59.0) <  luge_bound  ; ++e59){
      mpz_class  p59 = p53 *  intpow(59, e59) ;
      double luge59 = luge53 + e59 * log(59.0)  ; 

    for( int e61 = 0; e61 <= e59 && luge59 + e61 * log(61.0) <  luge_bound  ; ++e61){
      mpz_class  p61 = p59 *  intpow(61, e61) ;
      double luge61 = luge59 + e61 * log(61.0)  ; 

    for( int e67 = 0; e67 <= e61 && luge61 + e67 * log(67.0) <  luge_bound  ; ++e67){
      mpz_class  p67 = p61 *  intpow(67, e67) ;
      double luge67 = luge61 + e67 * log(67.0)  ; 

    for( int e71 = 0; e71 <= e67 && luge67 + e71 * log(71.0) <  luge_bound  ; ++e71){
      mpz_class  p71 = p67 *  intpow(71, e71) ;
      double luge71 = luge67 + e71 * log(71.0)  ; 

    for( int e73 = 0; e73 <= e71 && luge71 + e73 * log(73.0) <  luge_bound  ; ++e73){
      mpz_class  p73 = p71 *  intpow(73, e73) ;
      double luge73 = luge71 + e73 * log(73.0)  ; 

    for( int e79 = 0; e79 <= e73 && luge73 + e79 * log(79.0) <  luge_bound  ; ++e79){
      mpz_class  p79 = p73 *  intpow(79, e79) ;
      double luge79 = luge73 + e79 * log(79.0)  ; 

    for( int e83 = 0; e83 <= e79 && luge79 + e83 * log(83.0) <  luge_bound  ; ++e83){
      mpz_class  p83 = p79 *  intpow(83, e83) ;
      double luge83 = luge79 + e83 * log(83.0)  ; 

    for( int e89 = 0; e89 <= e83 && luge83 + e89 * log(89.0) <  luge_bound  ; ++e89){
      mpz_class  p89 = p83 *  intpow(89, e89) ;
      double luge89 = luge83 + e89 * log(89.0)  ; 

    for( int e97 = 0; e97 <= e89 && luge89 + e97 * log(97.0) <  luge_bound  ; ++e97){
      mpz_class  p97 = p89 *  intpow(97, e97) ;
      double luge97 = luge89 + e97 * log(97.0)  ; 

    for( int e101 = 0; e101 <= e97 && luge97 + e101 * log(101.0) <  luge_bound  ; ++e101){
      mpz_class  p101 = p97 *  intpow(101, e101) ;
      double luge101 = luge97 + e101 * log(101.0)  ; 

    for( int e103 = 0; e103 <= e101 && luge101 + e103 * log(103.0) <  luge_bound  ; ++e103){
      mpz_class  p103 = p101 *  intpow(103, e103) ;
      double luge103 = luge101 + e103 * log(103.0)  ; 

    for( int e107 = 0; e107 <= e103 && luge103 + e107 * log(107.0) <  luge_bound  ; ++e107){
      mpz_class  p107 = p103 *  intpow(107, e107) ;
      double luge107 = luge103 + e107 * log(107.0)  ; 

    for( int e109 = 0; e109 <= e107 && luge107 + e109 * log(109.0) <  luge_bound  ; ++e109){
      mpz_class  p109 = p107 *  intpow(109, e109) ;
      double luge109 = luge107 + e109 * log(109.0)  ; 

    for( int e113 = 0; e113 <= e109 && luge109 + e113 * log(113.0) <  luge_bound  ; ++e113){
      mpz_class  p113 = p109 *  intpow(113, e113) ;
      double luge113 = luge109 + e113 * log(113.0)  ; 

    for( int e127 = 0; e127 <= e113 && luge113 + e127 * log(127.0) <  luge_bound  ; ++e127){
      mpz_class  p127 = p113 *  intpow(127, e127) ;
      double luge127 = luge113 + e127 * log(127.0)  ; 

    for( int e131 = 0; e131 <= e127 && luge127 + e131 * log(131.0) <  luge_bound  ; ++e131){
      mpz_class  p131 = p127 *  intpow(131, e131) ;
      double luge131 = luge127 + e131 * log(131.0)  ; 

    for( int e137 = 0; e137 <= e131 && luge131 + e137 * log(137.0) <  luge_bound  ; ++e137){
      mpz_class  p137 = p131 *  intpow(137, e137) ;
      double luge137 = luge131 + e137 * log(137.0)  ; 

    for( int e139 = 0; e139 <= e137 && luge137 + e139 * log(139.0) <  luge_bound  ; ++e139){
      mpz_class  p139 = p137 *  intpow(139, e139) ;
      double luge139 = luge137 + e139 * log(139.0)  ; 

    for( int e149 = 0; e149 <= e139 && luge139 + e149 * log(149.0) <  luge_bound  ; ++e149){
      mpz_class  p149 = p139 *  intpow(149, e149) ;
      double luge149 = luge139 + e149 * log(149.0)  ; 


//  g++  -o joseph joseph.cc  -lgmp -lgmpxx
 
     mpz_class p = p149;
     double luge = luge149;

    if (   orourke(orourke(orourke(orourke(orourke(p))))) != 1 &&    orourke(orourke(orourke(orourke(orourke(orourke(p)))))) == 1  && luge < luge_bound  ) 
    {
          cout <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " << orourke(p) << endl;
         luge_bound = luge;
  
           ofstream outfile("joseph.txt",ios::app);
         outfile <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " <<   orourke(p)  << " " <<    orourke(orourke(p)) << endl;
        
        outfile.close();  // close quickly save partial progress
       system("date >> joseph.txt") ;


  
    } // if

   } // 149
   } // 139
   } // 137
   } // 131
   } // 127
   } // 113
   } // 109
   } // 107
   } // 103
   } // 101
   } // 97
   } // 89
   } // 83
   } // 79
   } // 73
   } // 71
   } // 67
   } // 61
   } // 59
   } // 53
   } // 47
   } // 43
   } // 41
   } // 37
   } // 31
   } // 29
   } // 23
   } // 19
   } // 17
   } // 13
   } // 11
   } // 7
   } // 5
   } // 3
   } // 2


    return 0 ;
}

    #include <iostream>
    #include <stdlib.h>
    #include <fstream>
    #include <sstream>
    #include <strstream>
    #include <list>
    #include <set>
    #include <math.h>
    #include <iomanip>
    #include <string>
    #include <algorithm>
    #include <iterator>
    
    
    #include <gmp.h>
    #include <gmpxx.h>
    
    using namespace std;
    
    
    
    
    // const double my_pi = 4 * atan(1.0);
    const double E_TO_THE_GAMMA  = 1.7810724179901979852365 ;
    const double GAMMA  = 0.57721566490153286060 ;
    const int BOUND = 1875;
    
    //  joseph.cc   
    
    
    
    
    //  g++  -o joseph joseph.cc  -lgmp -lgmpxx
    
     
    
    string stringify(int x)
     {
       ostringstream o;
       o << x  ;
       return o.str();
     }
     
    
     
     
     
    string mp_Factored( mpz_class  i)
    {
      string fac;
      fac = " = ";
      int p = 2;
       mpz_class  temp = i;
      if (temp < 0 )
      {
        temp *= -1;
        fac += " -1 * ";
      }
     
      if ( 1 == temp) fac += " 1 ";
      if ( temp > 1)
      {
        int primefac = 0;
        while( temp > 1 && p * p <= temp)
        {
          if (temp % p == 0)
          {
            ++primefac;
            if (primefac > 1) fac += " ";
             fac += stringify( p) ;
            temp /= p;
            int exponent = 1;
            while (temp % p == 0)
            {
              temp /= p;
              ++exponent;
            } // while p is fac
            if ( exponent > 1)
            {
              fac += "^" ;
              fac += stringify( exponent) ;
            }
          }  // if p is factor
          ++p;
        } // while p
        if (temp > 1 && primefac >= 1) fac += " ";
        if (temp > 1 ) fac += stringify( temp.get_ui())  ;
      } // temp > 1
      return fac;
    } // mp_Factored
    
    
    
    //  g++  -o joseph joseph.cc  -lgmp -lgmpxx
    
     
     mpz_class  intpow(int n, int k)
    {
        mpz_class blob = 1;
       for(int j = 1; j <= k; ++j) blob *= n;
    
       return ( blob );
    
    }
    
    
     mpz_class orourke( mpz_class i)
    {
      mpz_class joe = 1;
     
      int p = 2;
      mpz_class temp = i;
      if (temp < 0 )
      {
        temp *= -1;
       
      }
     
    
      if ( temp > 1)
      {
        
        while( temp > 1 && p * p <= temp)
        {
          if (temp % p == 0)
          {
       
            temp /= p;
            int exponent = 1;
            while (temp % p == 0)
            {
              temp /= p;
              ++exponent;
            } // while p is fac
            if ( exponent > 1)
            {
            
              joe *= exponent ;
            }
          }  // if p is factor
          ++p;
        } // while p
       
      } // temp > 1
      return joe;
    } // orourke
    
    
    
    //  g++  -o joseph joseph.cc  -lgmp -lgmpxx
    
    
    int main()
    {
     
       ofstream erasefile("joseph.txt");
      erasefile.close();
    
    
    
  //      double luge = 0.0; // declared later although compile did not complain
      double luge_bound = 270.0;  //270.0
         // product of exponents
       for( int e2 = 2; e2 * log(2.0) <  luge_bound  ; ++e2){
          mpz_class  p2 =   intpow(2, e2) ;
          double luge2 =   e2 * log(2.0) ; 
    
     //   cerr << "2^" << e2 << endl;
     
        for( int e3 = 0; e3 <= e2 && luge2 + e3 * log(3.0) <  luge_bound  ; ++e3){
          mpz_class  p3 = p2 *  intpow(3, e3) ;
          double luge3 = luge2 + e3 * log(3.0)  ; 
     
     //   cerr << "2^" << e2 << "  3^" << e3 << endl;
    
        for( int e5 = 0; e5 <= e3 && luge3 + e5 * log(5.0) <  luge_bound  ; ++e5){
          mpz_class  p5 = p3 *  intpow(5, e5) ;
          double luge5 = luge3 + e5 * log(5.0)  ; 
    
     //   cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5 << endl;
    
        for( int e7 = 0; e7 <= e5 && luge5 + e7 * log(7.0) <  luge_bound  ; ++e7){
          mpz_class  p7 = p5 *  intpow(7, e7) ;
          double luge7 = luge5 + e7 * log(7.0)  ; 
    
        cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5  << "  7^" << e7  << endl;
           system("date");
             cout << endl;
    
    
    
        for( int e11 = 0; e11 <= e7 && luge7 + e11 * log(11.0) <  luge_bound  ; ++e11){
          mpz_class  p11 = p7 *  intpow(11, e11) ;
          double luge11 = luge7 + e11 * log(11.0)  ; 
    
        for( int e13 = 0; e13 <= e11 && luge11 + e13 * log(13.0) <  luge_bound  ; ++e13){
          mpz_class  p13 = p11 *  intpow(13, e13) ;
          double luge13 = luge11 + e13 * log(13.0)  ; 
    
        for( int e17 = 0; e17 <= e13 && luge13 + e17 * log(17.0) <  luge_bound  ; ++e17){
          mpz_class  p17 = p13 *  intpow(17, e17) ;
          double luge17 = luge13 + e17 * log(17.0)  ; 
    
        for( int e19 = 0; e19 <= e17 && luge17 + e19 * log(19.0) <  luge_bound  ; ++e19){
          mpz_class  p19 = p17 *  intpow(19, e19) ;
          double luge19 = luge17 + e19 * log(19.0)  ; 
    
        for( int e23 = 0; e23 <= e19 && luge19 + e23 * log(23.0) <  luge_bound  ; ++e23){
          mpz_class  p23 = p19 *  intpow(23, e23) ;
          double luge23 = luge19 + e23 * log(23.0)  ; 
        
        for( int e29 = 0; e29 <= e23 && luge23 + e29 * log(29.0) <  luge_bound  ; ++e29){
          mpz_class  p29 = p23 *  intpow(29, e29) ;
          double luge29 = luge23 + e29 * log(29.0)  ; 
        
        for( int e31 = 0; e31 <= e29 && luge29 + e31 * log(31.0) <  luge_bound  ; ++e31){
          mpz_class  p31 = p29 *  intpow(31, e31) ;
          double luge31 = luge29 + e31 * log(31.0)  ; 
    
        for( int e37 = 0; e37 <= e31 && luge31 + e37 * log(37.0) <  luge_bound  ; ++e37){
          mpz_class  p37 = p31 *  intpow(37, e37) ;
          double luge37 = luge31 + e37 * log(37.0)  ; 
    
        for( int e41 = 0; e41 <= e37 && luge37 + e41 * log(41.0) <  luge_bound  ; ++e41){
          mpz_class  p41 = p37 *  intpow(41, e41) ;
          double luge41 = luge37 + e41 * log(41.0)  ; 
    
        for( int e43 = 0; e43 <= e41 && luge41 + e43 * log(43.0) <  luge_bound  ; ++e43){
          mpz_class  p43 = p41 *  intpow(43, e43) ;
          double luge43 = luge41 + e43 * log(43.0)  ; 
    
        for( int e47 = 0; e47 <= e43 && luge43 + e47 * log(47.0) <  luge_bound  ; ++e47){
          mpz_class  p47 = p43 *  intpow(47, e47) ;
          double luge47 = luge43 + e47 * log(47.0)  ; 
    
        for( int e53 = 0; e53 <= e47 && luge47 + e53 * log(53.0) <  luge_bound  ; ++e53){
          mpz_class  p53 = p47 *  intpow(53, e53) ;
          double luge53 = luge47 + e53 * log(53.0)  ; 
    
        for( int e59 = 0; e59 <= e53 && luge53 + e59 * log(59.0) <  luge_bound  ; ++e59){
          mpz_class  p59 = p53 *  intpow(59, e59) ;
          double luge59 = luge53 + e59 * log(59.0)  ; 
    
        for( int e61 = 0; e61 <= e59 && luge59 + e61 * log(61.0) <  luge_bound  ; ++e61){
          mpz_class  p61 = p59 *  intpow(61, e61) ;
          double luge61 = luge59 + e61 * log(61.0)  ; 
    
        for( int e67 = 0; e67 <= e61 && luge61 + e67 * log(67.0) <  luge_bound  ; ++e67){
          mpz_class  p67 = p61 *  intpow(67, e67) ;
          double luge67 = luge61 + e67 * log(67.0)  ; 
    
        for( int e71 = 0; e71 <= e67 && luge67 + e71 * log(71.0) <  luge_bound  ; ++e71){
          mpz_class  p71 = p67 *  intpow(71, e71) ;
          double luge71 = luge67 + e71 * log(71.0)  ; 
    
        for( int e73 = 0; e73 <= e71 && luge71 + e73 * log(73.0) <  luge_bound  ; ++e73){
          mpz_class  p73 = p71 *  intpow(73, e73) ;
          double luge73 = luge71 + e73 * log(73.0)  ; 
    
        for( int e79 = 0; e79 <= e73 && luge73 + e79 * log(79.0) <  luge_bound  ; ++e79){
          mpz_class  p79 = p73 *  intpow(79, e79) ;
          double luge79 = luge73 + e79 * log(79.0)  ; 
    
        for( int e83 = 0; e83 <= e79 && luge79 + e83 * log(83.0) <  luge_bound  ; ++e83){
          mpz_class  p83 = p79 *  intpow(83, e83) ;
          double luge83 = luge79 + e83 * log(83.0)  ; 
    
        for( int e89 = 0; e89 <= e83 && luge83 + e89 * log(89.0) <  luge_bound  ; ++e89){
          mpz_class  p89 = p83 *  intpow(89, e89) ;
          double luge89 = luge83 + e89 * log(89.0)  ; 
    
        for( int e97 = 0; e97 <= e89 && luge89 + e97 * log(97.0) <  luge_bound  ; ++e97){
          mpz_class  p97 = p89 *  intpow(97, e97) ;
          double luge97 = luge89 + e97 * log(97.0)  ; 
    
        for( int e101 = 0; e101 <= e97 && luge97 + e101 * log(101.0) <  luge_bound  ; ++e101){
          mpz_class  p101 = p97 *  intpow(101, e101) ;
          double luge101 = luge97 + e101 * log(101.0)  ; 
    
        for( int e103 = 0; e103 <= e101 && luge101 + e103 * log(103.0) <  luge_bound  ; ++e103){
          mpz_class  p103 = p101 *  intpow(103, e103) ;
          double luge103 = luge101 + e103 * log(103.0)  ; 
    
        for( int e107 = 0; e107 <= e103 && luge103 + e107 * log(107.0) <  luge_bound  ; ++e107){
          mpz_class  p107 = p103 *  intpow(107, e107) ;
          double luge107 = luge103 + e107 * log(107.0)  ; 
    
        for( int e109 = 0; e109 <= e107 && luge107 + e109 * log(109.0) <  luge_bound  ; ++e109){
          mpz_class  p109 = p107 *  intpow(109, e109) ;
          double luge109 = luge107 + e109 * log(109.0)  ; 
    
        for( int e113 = 0; e113 <= e109 && luge109 + e113 * log(113.0) <  luge_bound  ; ++e113){
          mpz_class  p113 = p109 *  intpow(113, e113) ;
          double luge113 = luge109 + e113 * log(113.0)  ; 
    
        for( int e127 = 0; e127 <= e113 && luge113 + e127 * log(127.0) <  luge_bound  ; ++e127){
          mpz_class  p127 = p113 *  intpow(127, e127) ;
          double luge127 = luge113 + e127 * log(127.0)  ; 
    
        for( int e131 = 0; e131 <= e127 && luge127 + e131 * log(131.0) <  luge_bound  ; ++e131){
          mpz_class  p131 = p127 *  intpow(131, e131) ;
          double luge131 = luge127 + e131 * log(131.0)  ; 
    
        for( int e137 = 0; e137 <= e131 && luge131 + e137 * log(137.0) <  luge_bound  ; ++e137){
          mpz_class  p137 = p131 *  intpow(137, e137) ;
          double luge137 = luge131 + e137 * log(137.0)  ; 
    
        for( int e139 = 0; e139 <= e137 && luge137 + e139 * log(139.0) <  luge_bound  ; ++e139){
          mpz_class  p139 = p137 *  intpow(139, e139) ;
          double luge139 = luge137 + e139 * log(139.0)  ; 
    
        for( int e149 = 0; e149 <= e139 && luge139 + e149 * log(149.0) <  luge_bound  ; ++e149){
          mpz_class  p149 = p139 *  intpow(149, e149) ;
          double luge149 = luge139 + e149 * log(149.0)  ; 
    
    
    //  g++  -o joseph joseph.cc  -lgmp -lgmpxx
    
         mpz_class p = p149;
         double luge = luge149;
    
        if (   orourke(orourke(orourke(orourke(orourke(p))))) != 1 &&    orourke(orourke(orourke(orourke(orourke(orourke(p)))))) == 1  && luge < luge_bound  ) 
        {
              cout <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " << orourke(p) << endl;
             luge_bound = luge;
      
               ofstream outfile("joseph.txt",ios::app);
             outfile <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " <<   orourke(p)  << " " <<    orourke(orourke(p)) << endl;
            
            outfile.close();  // close quickly save partial progress
           system("date >> joseph.txt") ;
    
    
      
        } // if
    
       } // 149
       } // 139
       } // 137
       } // 131
       } // 127
       } // 113
       } // 109
       } // 107
       } // 103
       } // 101
       } // 97
       } // 89
       } // 83
       } // 79
       } // 73
       } // 71
       } // 67
       } // 61
       } // 59
       } // 53
       } // 47
       } // 43
       } // 41
       } // 37
       } // 31
       } // 29
       } // 23
       } // 19
       } // 17
       } // 13
       } // 11
       } // 7
       } // 5
       } // 3
       } // 2
    
    
        return 0 ;
    }
Source Link
Will Jagy
Will Jagy
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Got a correct program going to find $m(6).$ Today is Monday, 7 October, 2013. I call it joseph.cc I started it going at 12:53 PDT, lunchtime, and put timestamps into the file that keeps the successes (of smaller size as we continue) called joseph.txt. I switched to log 10 for the output. Anyway, readable or not, here is output for the first 17 minutes, followed by the program in its entirety:

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

jagy@phobeusjunior:~$ tail -45 joseph.txt
     116.814  651907611648300222725782474725592418809035465656889971919224893561886421964804482955701436492603438100109520590000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^3 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^2 71^2 73^2 79^2 83^2 89^2 97^2 101^2 17283248640000 1296
Mon Oct  7 12:58:36 PDT 2013
     116.094  124169835254646341805332354513462020365253985861321166105191056581780738935164700557095176071476176867808332370000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^3 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^2 73^2 79^2 83^2 89^2 97^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     115.463  29046424422943628261615103866949719080021683800698043001118664633489149367233234767368103149465306120315244930000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 89^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.996  9904607040319497529935916619698420809889984591047268545135906220812295472907078286410964096289078630346102330000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 83^2 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.668  4656847467498164102113867605051993758634585584323138745492117905241838443423722829102208260688100694395561830000000 = 2^7 3^7 5^7 7^5 11^5 13^5 17^5 19^4 23^4 29^4 31^4 37^4 41^4 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^3 17283248640000 1296
Mon Oct  7 12:58:37 PDT 2013
     114.533  3413990801383729063446996805975279442431534859039247321555545609617270301842462008385267520786794596391048230000000 = 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^3 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^2 79^2 83^2 15122842560000 1296
Mon Oct  7 12:59:31 PDT 2013
     114.127  1338538126656619567480089762365979064306514102811004066703662170355094656013425734453274433683427522841083070000000 = 2^7 3^7 5^7 7^7 11^5 13^5 17^5 19^5 23^4 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 79^2 15122842560000 1296
Mon Oct  7 12:59:31 PDT 2013
     114.077  1193767539331957140297096557815901213255897692075957159953947066206770846878821925647640682243543917983250820000000 = 2^8 3^7 5^7 7^7 11^7 13^5 17^5 19^5 23^5 29^4 31^4 37^4 41^3 43^3 47^3 53^3 59^3 61^3 67^3 71^3 73^3 15122842560000 1296
Mon Oct  7 13:04:22 PDT 2013
jagy@phobeusjunior:~$

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

#include <iostream>
#include <stdlib.h>
#include <fstream>
#include <sstream>
#include <strstream>
#include <list>
#include <set>
#include <math.h>
#include <iomanip>
#include <string>
#include <algorithm>
#include <iterator>


#include <gmp.h>
#include <gmpxx.h>

using namespace std;




// const double my_pi = 4 * atan(1.0);
const double E_TO_THE_GAMMA  = 1.7810724179901979852365 ;
const double GAMMA  = 0.57721566490153286060 ;
const int BOUND = 1875;

//  joseph.cc   




//  g++  -o joseph joseph.cc  -lgmp -lgmpxx



string stringify(int x)
 {
   ostringstream o;
   o << x  ;
   return o.str();
 }





string mp_Factored( mpz_class  i)
{
  string fac;
  fac = " = ";
  int p = 2;
   mpz_class  temp = i;
  if (temp < 0 )
  {
    temp *= -1;
    fac += " -1 * ";
  }

  if ( 1 == temp) fac += " 1 ";
  if ( temp > 1)
  {
    int primefac = 0;
    while( temp > 1 && p * p <= temp)
    {
      if (temp % p == 0)
      {
        ++primefac;
        if (primefac > 1) fac += " ";
         fac += stringify( p) ;
        temp /= p;
        int exponent = 1;
        while (temp % p == 0)
        {
          temp /= p;
          ++exponent;
        } // while p is fac
        if ( exponent > 1)
        {
          fac += "^" ;
          fac += stringify( exponent) ;
        }
      }  // if p is factor
      ++p;
    } // while p
    if (temp > 1 && primefac >= 1) fac += " ";
    if (temp > 1 ) fac += stringify( temp.get_ui())  ;
  } // temp > 1
  return fac;
} // mp_Factored



//  g++  -o joseph joseph.cc  -lgmp -lgmpxx


 mpz_class  intpow(int n, int k)
{
    mpz_class blob = 1;
   for(int j = 1; j <= k; ++j) blob *= n;

   return ( blob );

}


 mpz_class orourke( mpz_class i)
{
  mpz_class joe = 1;
 
  int p = 2;
  mpz_class temp = i;
  if (temp < 0 )
  {
    temp *= -1;
  
  }


  if ( temp > 1)
  {
   
    while( temp > 1 && p * p <= temp)
    {
      if (temp % p == 0)
      {
   
        temp /= p;
        int exponent = 1;
        while (temp % p == 0)
        {
          temp /= p;
          ++exponent;
        } // while p is fac
        if ( exponent > 1)
        {
        
          joe *= exponent ;
        }
      }  // if p is factor
      ++p;
    } // while p
   
  } // temp > 1
  return joe;
} // orourke



//  g++  -o joseph joseph.cc  -lgmp -lgmpxx


int main()
{

   ofstream erasefile("joseph.txt");
  erasefile.close();



    double luge = 0.0;
  double luge_bound = 270.0;  //270.0
     // product of exponents
   for( int e2 = 2; e2 * log(2.0) <  luge_bound  ; ++e2){
      mpz_class  p2 =   intpow(2, e2) ;
      double luge2 =   e2 * log(2.0) ; 

 //   cerr << "2^" << e2 << endl;

    for( int e3 = 0; e3 <= e2 && luge2 + e3 * log(3.0) <  luge_bound  ; ++e3){
      mpz_class  p3 = p2 *  intpow(3, e3) ;
      double luge3 = luge2 + e3 * log(3.0)  ; 

 //   cerr << "2^" << e2 << "  3^" << e3 << endl;

    for( int e5 = 0; e5 <= e3 && luge3 + e5 * log(5.0) <  luge_bound  ; ++e5){
      mpz_class  p5 = p3 *  intpow(5, e5) ;
      double luge5 = luge3 + e5 * log(5.0)  ; 

 //   cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5 << endl;

    for( int e7 = 0; e7 <= e5 && luge5 + e7 * log(7.0) <  luge_bound  ; ++e7){
      mpz_class  p7 = p5 *  intpow(7, e7) ;
      double luge7 = luge5 + e7 * log(7.0)  ; 

    cerr << "2^" << e2 << "  3^" << e3  << "  5^" << e5  << "  7^" << e7  << endl;
       system("date");
         cout << endl;



    for( int e11 = 0; e11 <= e7 && luge7 + e11 * log(11.0) <  luge_bound  ; ++e11){
      mpz_class  p11 = p7 *  intpow(11, e11) ;
      double luge11 = luge7 + e11 * log(11.0)  ; 

    for( int e13 = 0; e13 <= e11 && luge11 + e13 * log(13.0) <  luge_bound  ; ++e13){
      mpz_class  p13 = p11 *  intpow(13, e13) ;
      double luge13 = luge11 + e13 * log(13.0)  ; 

    for( int e17 = 0; e17 <= e13 && luge13 + e17 * log(17.0) <  luge_bound  ; ++e17){
      mpz_class  p17 = p13 *  intpow(17, e17) ;
      double luge17 = luge13 + e17 * log(17.0)  ; 

    for( int e19 = 0; e19 <= e17 && luge17 + e19 * log(19.0) <  luge_bound  ; ++e19){
      mpz_class  p19 = p17 *  intpow(19, e19) ;
      double luge19 = luge17 + e19 * log(19.0)  ; 

    for( int e23 = 0; e23 <= e19 && luge19 + e23 * log(23.0) <  luge_bound  ; ++e23){
      mpz_class  p23 = p19 *  intpow(23, e23) ;
      double luge23 = luge19 + e23 * log(23.0)  ; 
    
    for( int e29 = 0; e29 <= e23 && luge23 + e29 * log(29.0) <  luge_bound  ; ++e29){
      mpz_class  p29 = p23 *  intpow(29, e29) ;
      double luge29 = luge23 + e29 * log(29.0)  ; 
    
    for( int e31 = 0; e31 <= e29 && luge29 + e31 * log(31.0) <  luge_bound  ; ++e31){
      mpz_class  p31 = p29 *  intpow(31, e31) ;
      double luge31 = luge29 + e31 * log(31.0)  ; 

    for( int e37 = 0; e37 <= e31 && luge31 + e37 * log(37.0) <  luge_bound  ; ++e37){
      mpz_class  p37 = p31 *  intpow(37, e37) ;
      double luge37 = luge31 + e37 * log(37.0)  ; 

    for( int e41 = 0; e41 <= e37 && luge37 + e41 * log(41.0) <  luge_bound  ; ++e41){
      mpz_class  p41 = p37 *  intpow(41, e41) ;
      double luge41 = luge37 + e41 * log(41.0)  ; 

    for( int e43 = 0; e43 <= e41 && luge41 + e43 * log(43.0) <  luge_bound  ; ++e43){
      mpz_class  p43 = p41 *  intpow(43, e43) ;
      double luge43 = luge41 + e43 * log(43.0)  ; 

    for( int e47 = 0; e47 <= e43 && luge43 + e47 * log(47.0) <  luge_bound  ; ++e47){
      mpz_class  p47 = p43 *  intpow(47, e47) ;
      double luge47 = luge43 + e47 * log(47.0)  ; 

    for( int e53 = 0; e53 <= e47 && luge47 + e53 * log(53.0) <  luge_bound  ; ++e53){
      mpz_class  p53 = p47 *  intpow(53, e53) ;
      double luge53 = luge47 + e53 * log(53.0)  ; 

    for( int e59 = 0; e59 <= e53 && luge53 + e59 * log(59.0) <  luge_bound  ; ++e59){
      mpz_class  p59 = p53 *  intpow(59, e59) ;
      double luge59 = luge53 + e59 * log(59.0)  ; 

    for( int e61 = 0; e61 <= e59 && luge59 + e61 * log(61.0) <  luge_bound  ; ++e61){
      mpz_class  p61 = p59 *  intpow(61, e61) ;
      double luge61 = luge59 + e61 * log(61.0)  ; 

    for( int e67 = 0; e67 <= e61 && luge61 + e67 * log(67.0) <  luge_bound  ; ++e67){
      mpz_class  p67 = p61 *  intpow(67, e67) ;
      double luge67 = luge61 + e67 * log(67.0)  ; 

    for( int e71 = 0; e71 <= e67 && luge67 + e71 * log(71.0) <  luge_bound  ; ++e71){
      mpz_class  p71 = p67 *  intpow(71, e71) ;
      double luge71 = luge67 + e71 * log(71.0)  ; 

    for( int e73 = 0; e73 <= e71 && luge71 + e73 * log(73.0) <  luge_bound  ; ++e73){
      mpz_class  p73 = p71 *  intpow(73, e73) ;
      double luge73 = luge71 + e73 * log(73.0)  ; 

    for( int e79 = 0; e79 <= e73 && luge73 + e79 * log(79.0) <  luge_bound  ; ++e79){
      mpz_class  p79 = p73 *  intpow(79, e79) ;
      double luge79 = luge73 + e79 * log(79.0)  ; 

    for( int e83 = 0; e83 <= e79 && luge79 + e83 * log(83.0) <  luge_bound  ; ++e83){
      mpz_class  p83 = p79 *  intpow(83, e83) ;
      double luge83 = luge79 + e83 * log(83.0)  ; 

    for( int e89 = 0; e89 <= e83 && luge83 + e89 * log(89.0) <  luge_bound  ; ++e89){
      mpz_class  p89 = p83 *  intpow(89, e89) ;
      double luge89 = luge83 + e89 * log(89.0)  ; 

    for( int e97 = 0; e97 <= e89 && luge89 + e97 * log(97.0) <  luge_bound  ; ++e97){
      mpz_class  p97 = p89 *  intpow(97, e97) ;
      double luge97 = luge89 + e97 * log(97.0)  ; 

    for( int e101 = 0; e101 <= e97 && luge97 + e101 * log(101.0) <  luge_bound  ; ++e101){
      mpz_class  p101 = p97 *  intpow(101, e101) ;
      double luge101 = luge97 + e101 * log(101.0)  ; 

    for( int e103 = 0; e103 <= e101 && luge101 + e103 * log(103.0) <  luge_bound  ; ++e103){
      mpz_class  p103 = p101 *  intpow(103, e103) ;
      double luge103 = luge101 + e103 * log(103.0)  ; 

    for( int e107 = 0; e107 <= e103 && luge103 + e107 * log(107.0) <  luge_bound  ; ++e107){
      mpz_class  p107 = p103 *  intpow(107, e107) ;
      double luge107 = luge103 + e107 * log(107.0)  ; 

    for( int e109 = 0; e109 <= e107 && luge107 + e109 * log(109.0) <  luge_bound  ; ++e109){
      mpz_class  p109 = p107 *  intpow(109, e109) ;
      double luge109 = luge107 + e109 * log(109.0)  ; 

    for( int e113 = 0; e113 <= e109 && luge109 + e113 * log(113.0) <  luge_bound  ; ++e113){
      mpz_class  p113 = p109 *  intpow(113, e113) ;
      double luge113 = luge109 + e113 * log(113.0)  ; 

    for( int e127 = 0; e127 <= e113 && luge113 + e127 * log(127.0) <  luge_bound  ; ++e127){
      mpz_class  p127 = p113 *  intpow(127, e127) ;
      double luge127 = luge113 + e127 * log(127.0)  ; 

    for( int e131 = 0; e131 <= e127 && luge127 + e131 * log(131.0) <  luge_bound  ; ++e131){
      mpz_class  p131 = p127 *  intpow(131, e131) ;
      double luge131 = luge127 + e131 * log(131.0)  ; 

    for( int e137 = 0; e137 <= e131 && luge131 + e137 * log(137.0) <  luge_bound  ; ++e137){
      mpz_class  p137 = p131 *  intpow(137, e137) ;
      double luge137 = luge131 + e137 * log(137.0)  ; 

    for( int e139 = 0; e139 <= e137 && luge137 + e139 * log(139.0) <  luge_bound  ; ++e139){
      mpz_class  p139 = p137 *  intpow(139, e139) ;
      double luge139 = luge137 + e139 * log(139.0)  ; 

    for( int e149 = 0; e149 <= e139 && luge139 + e149 * log(149.0) <  luge_bound  ; ++e149){
      mpz_class  p149 = p139 *  intpow(149, e149) ;
      double luge149 = luge139 + e149 * log(149.0)  ; 


//  g++  -o joseph joseph.cc  -lgmp -lgmpxx

     mpz_class p = p149;
     double luge = luge149;

    if (   orourke(orourke(orourke(orourke(orourke(p))))) != 1 &&    orourke(orourke(orourke(orourke(orourke(orourke(p)))))) == 1  && luge < luge_bound  ) 
    {
          cout <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " << orourke(p) << endl;
         luge_bound = luge;
  
           ofstream outfile("joseph.txt",ios::app);
         outfile <<  setw(12) << luge / log(10.0) << "  "  << p << mp_Factored(p) << " " <<   orourke(p)  << " " <<    orourke(orourke(p)) << endl;
        
        outfile.close();  // close quickly save partial progress
       system("date >> joseph.txt") ;


  
    } // if

   } // 149
   } // 139
   } // 137
   } // 131
   } // 127
   } // 113
   } // 109
   } // 107
   } // 103
   } // 101
   } // 97
   } // 89
   } // 83
   } // 79
   } // 73
   } // 71
   } // 67
   } // 61
   } // 59
   } // 53
   } // 47
   } // 43
   } // 41
   } // 37
   } // 31
   } // 29
   } // 23
   } // 19
   } // 17
   } // 13
   } // 11
   } // 7
   } // 5
   } // 3
   } // 2


    return 0 ;
}

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