Timeline for Moments of merit
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 11, 2018 at 21:08 | history | edited | David Feldman | CC BY-SA 4.0 |
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| May 10, 2018 at 0:49 | comment | added | David Feldman | @sylvain-julien Or perhaps $g_n/(\ln n)^2$. The heuristic: if x has primeness probability $1/\ln x$, then $\ln x$ consecutive composites starting at x should happen with probability about $(1 - 1/\ln x)^{\ln x}$, so $1/e$ in the limit. $c(\ln x)^2$ consecutive composites would occur with probability $1/e^{c\ln x}= 1/x^c$ making the expected number of occurrences finite for $c>1$. Thus one might expect a bound for my proposed quantity and even ask whether a particular gap realizes a maximum value. | |
| May 7, 2018 at 20:02 | comment | added | Sylvain JULIEN | Maybe the quantity defined by $ \log g_{n}/\log\log n $ where $ g_{n}=p_{n+1}-p_{n} $ can be of interest too. | |
| May 7, 2018 at 19:56 | history | edited | GH from MO |
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| May 7, 2018 at 17:27 | comment | added | David Feldman | There is also the Cramér–Shanks–Granville ratio, a candidate for a different normalized prime gap. | |
| May 7, 2018 at 17:26 | comment | added | David Feldman | I picked up the term from en.wikipedia.org/wiki/Prime_gap | |
| May 7, 2018 at 16:55 | comment | added | Greg Martin | I don't think "merit" is a term commonly used for this concept; "normalized prime gap" is common and quite descriptive. | |
| May 7, 2018 at 14:16 | vote | accept | David Feldman | ||
| May 7, 2018 at 7:50 | answer | added | Greg Martin | timeline score: 11 | |
| May 7, 2018 at 6:18 | history | asked | David Feldman | CC BY-SA 4.0 |