Timeline for An estimate for 'almost primes'?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 9, 2011 at 16:05 | vote | accept | Stanley Yao Xiao | ||
| Feb 8, 2011 at 23:32 | comment | added | Gerry Myerson | @Peter, I thought of that argument, but doesn't it count each almost prime twice? leading to an estimate that's off by a factor of 2? | |
| Feb 8, 2011 at 6:33 | comment | added | Péter Komjáth | Yes. For a prime $p\leq x$ the number of number of the form $pq\leq x$ where $q$ is prime is roughly $(x/p)/\log (x/p)$, which, when added up, is around $Sx/\log x$ where $S$ is the sum of the reciprocals of the primes up to $x$, which is $\log \log x$. | |
| Feb 8, 2011 at 4:02 | comment | added | Stanley Yao Xiao | Is there any 'quick and dirty' way of seeing that asymptotic? | |
| Feb 8, 2011 at 3:48 | comment | added | Michael Lugo | The On-Line Encyclopedia of Integer Sequences ( oeis.org/A001358) agrees with your estimate for the nth almost prime, and gives sources. | |
| Feb 8, 2011 at 2:27 | history | answered | Gerry Myerson | CC BY-SA 2.5 |