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:
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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
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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)
{
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 ;
}
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