Timeline for Why do primes dislike dividing the sum of all the preceding primes?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Mar 25, 2019 at 18:41 | history | suggested | CommunityBot | CC BY-SA 4.0 |
link Mertens' (not Merten's) eponymous thingies
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| Mar 25, 2019 at 17:52 | review | Suggested edits | |||
| S Mar 25, 2019 at 18:41 | |||||
| Feb 19, 2014 at 11:25 | comment | added | Hans Lundmark | (Nitpicking: The guy's name was Mertens, not Merten.) | |
| Jan 22, 2014 at 23:53 | comment | added | Filippo Alberto Edoardo | Thanks, I did not intepret the $1/p$ as being the sentence "lie in one of the $p$ classes $\mod{p}$". | |
| Feb 3, 2013 at 8:23 | vote | accept | Nilotpal Kanti Sinha | ||
| Feb 2, 2013 at 12:48 | comment | added | user9072 | @Filippo Alberto Edoardo: It is a heuristic (as said in the answer) but one that in this cases seems to make perfect sense: the sum of the primes preceeding $p$ is a number significantly larger than $p$ (about size $p^2/ (2 \log p)$ , I think) and there seems no reason for it being biased towards being in any particular residue class moduo $p$; so that it is $0$ mod $p$ seems just as likely as it being anything else, so prop. $1/p$ for it being $0$, ie divisible by $p$. This is the natural heuristic in this case, and explains the scarcity. To make this heuristic precise, seems very hard. | |
| Feb 2, 2013 at 0:52 | comment | added | Filippo Alberto Edoardo | Why is the probability $1/p$? | |
| Feb 1, 2013 at 20:18 | comment | added | Theo Johnson-Freyd | So the point is that any problem like this must be compared to $\log \log N$. But to get any good estimates of the comparison is extremely hard, because $\log\log N$ is so much smaller than $\infty$. For example, in the problem above, based on $N = 10^9$, we could argue that in fact primes very much do like to divide the sum of their predecessors, as there are in fact 5 primes with this property, which is fifty percent more than the expected number. | |
| Feb 1, 2013 at 12:41 | history | answered | David E Speyer | CC BY-SA 3.0 |