Timeline for Upper bound of number of prime factors
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2023 at 21:08 | comment | added | Terry Tao | Also, since one has $\omega(m) \gg \frac{\log m}{\log \log m}$ for infinitely many $m$ (in particular, primorials), it follows from Linnik's theorem that one also has $\omega(n) \gg \frac{\log n}{\log \log n}$ for any infinitely many $n$ of the form $p-1$ (take $p$ to be the first prime in the progression $1 \hbox{ mod } m$ for $m$ a primorial; Linnik's theorem tells us that $\log (p-1) \asymp \log n$). en.wikipedia.org/wiki/Linnik%27s_theorem . So the upper bound $\omega(n) \ll \frac{\log n}{\log\log n}$ is sharp up to constants for $n=p-1$. | |
| Apr 22, 2023 at 16:00 | comment | added | Joshua Stucky | @OfirGorodetsky Ahh, didn't see that typo. Corrected! | |
| Apr 22, 2023 at 16:00 | history | edited | Joshua Stucky | CC BY-SA 4.0 |
deleted 5 characters in body
|
| Apr 22, 2023 at 10:48 | comment | added | Ofir Gorodetsky | @JoshuaStucky I deleted my first comment because it was not actually accurate in terms of describing the papers I mentioned (feel free to delete yours as well). I wrote it because the last line of the answer mentions "prime factors" where I think it should be "divisors". | |
| Apr 22, 2023 at 5:33 | vote | accept | meirgold | ||
| Apr 22, 2023 at 5:20 | comment | added | Anurag Sahay | It's worth probably pointing out that @OfirGorodetsky's previous answer here ( mathoverflow.net/a/436137 ) is also relevant, especially the remarks about the central limit theorem. | |
| Apr 22, 2023 at 0:39 | history | answered | Joshua Stucky | CC BY-SA 4.0 |