Timeline for Are there any notion of 'almost primes' known to have small gaps?
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| when toggle format | what | by | license | comment | |
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| Dec 27, 2017 at 16:15 | comment | added | Gerry Myerson | There are bounds on the gap between numbers that are the sum of two squares (this is a natural superset of the primes congruent to 1 modulo 4). | |
| Dec 27, 2017 at 1:17 | history | edited | GH from MO |
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| Dec 26, 2017 at 21:45 | comment | added | Sylvain JULIEN | I wouldn't be that surprised that the set of integers where the Von Mangoldt function doesn't vanish (hence the union of primes and prime powers) behaves the way you want. | |
| Dec 26, 2017 at 20:48 | answer | added | Dan Brumleve | timeline score: 5 | |
| Feb 9, 2011 at 0:35 | comment | added | user9072 | It is not quite clear to me what you are looking for (and even if it were chances are I could not answer). Still, a small remark in the hope it is relevant: If you restrict the number of prime factors, say by $k$, you will get about $(x/log x) (\log \log x)^{k-1}$ elements below $x$. So, the gaps on avarage cannot be too small, roughly I guess also some $\log x$ times some quotient of iterate $\log$ factors. On the other hand there will be small gaps too. Thus, the gaps will remain quite non-uniform in size. | |
| Feb 8, 2011 at 22:27 | answer | added | Micah Milinovich | timeline score: 14 | |
| Feb 8, 2011 at 21:54 | comment | added | Luis H Gallardo | Considering only odd primes. Odd numbers have small gaps, all equal $2.$ | |
| Feb 8, 2011 at 21:06 | history | asked | Stanley Yao Xiao♦ | CC BY-SA 2.5 |