Timeline for How much space between these smooth numbers?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2016 at 22:15 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 21, 2016 at 23:43 | comment | added | Gerhard Paseman | Looking at maximal gaps (so we have first occurrence of gap g has g many rough numbers below n), my unverified program has (7,8), (9,374), (10,1116), (12,1421), (13,2940), (16,6992), all the way up to (40,26173683). I am finding some of these gaps do not have any 3 mod 4 primes in them. I am now hoping for C(n) to be O(log n). Gerhard "Still Hoping And Hanging On" Paseman, 2016.11.21. | |
| Nov 21, 2016 at 22:05 | answer | added | Jan-Christoph Schlage-Puchta | timeline score: 2 | |
| Nov 21, 2016 at 21:52 | comment | added | Gerry Myerson | OEIS points to "D. H. Greene and D. E. Knuth, Mathematics for the Analysis of Algorithms; see pp. 95-98." I don't have the book handy to see whether it answers the questions. | |
| Nov 21, 2016 at 21:45 | comment | added | Gerry Myerson | Primes have density zero, a fortiori squares of primes have density zero, so, yes, the answer is $1-\log2$. | |
| Nov 21, 2016 at 21:43 | history | edited | Gerry Myerson | CC BY-SA 3.0 |
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| Nov 21, 2016 at 20:10 | comment | added | Gerhard Paseman | It looks like the density should be the same as if we throw in the squares of primes. This would make the density 1- ln 2, and I would appreciate an undergraduate level reference for the result with prime squares. I still hope for the constant C. Gerhard "Dreams Of Nice Upper Bounds" Paseman, 2016.11.21. | |
| Nov 21, 2016 at 19:47 | history | asked | Gerhard Paseman | CC BY-SA 3.0 |