Timeline for Asymptotics for primality of sum of three consecutive primes
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 10, 2011 at 14:05 | comment | added | Noam D. Elkies | [correction: naturally what I meant is the sum over $m$ of $1/\log(3p_m)$, not $1/\log(3p_n)$.] | |
| Aug 10, 2011 at 13:58 | comment | added | Noam D. Elkies | It may seem from this data that $2.30...$ is too large, but there are several small-number effects here. $n/\log n$ should be $\sum_{m=1}^n 1/\log(3 p_n)$, which is asymptotically the same but still smaller by $24\%$ at $n=10^5$ (6589 vs. 8686). This makes $R(10^5) = 18892$ seem too large by a substantial margin. It turns out that for small $n$ and the smallest odd primes $l$ it's much rarer than expected to have $l\mid p_n+p_{n+1}+p_{n+2}$; e.g. up to $10^5$ we get only $16401$ for $l=3$ and $15856$ for $l=5$, not the expected $25000$ and $18750$. Presumably this decays for large $n$... | |
| Aug 10, 2011 at 10:36 | history | edited | Álvaro Lozano-Robledo | CC BY-SA 3.0 |
deleted 91 characters in body
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| Aug 10, 2011 at 4:21 | history | answered | Álvaro Lozano-Robledo | CC BY-SA 3.0 |