Timeline for Is every prime the largest prime factor in some prime gap?
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 21, 2019 at 19:39 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
deleted 7 characters in body
|
| Dec 17, 2019 at 7:31 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
added 2 characters in body
|
| Dec 14, 2019 at 8:02 | history | edited | Martin Sleziak |
edited tags
|
|
| Dec 14, 2019 at 7:59 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
deleted 2 characters in body
|
| Dec 11, 2019 at 14:04 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
added 2 characters in body
|
| Dec 11, 2019 at 1:16 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
deleted 2 characters in body
|
| Dec 10, 2019 at 16:03 | comment | added | Gerhard Paseman | Now that I see it, I realize that rough numbers only occur about 70% of the time, and so prime gap intervals full of non rough numbers (numbers with largest prime factor less than its square root) should occur, meaning a prevalence of k larger than 2. I think the fact that primes greater than 3 are underrepresented is interesting, and possibly temporary. Gerhard "Looks Forward To Gap Data" Paseman, 2019.12.10. | |
| Dec 10, 2019 at 15:32 | comment | added | Nilotpal Kanti Sinha | @GerhardPaseman Check the data in the answer below | |
| Dec 10, 2019 at 9:39 | answer | added | Space | timeline score: 5 | |
| Dec 10, 2019 at 5:33 | comment | added | Gerhard Paseman | Further, I am happy to see smaller snapshots at the beginning, and guess what the later values will be. If you can print out data at powers of 10 greater than 10^4, that would be more informative. Gerhard "Likes To See Data Grow" Paseman, 2019.12.09. | |
| Dec 10, 2019 at 5:30 | comment | added | Gerhard Paseman | To be honest, I won't know till I see the data. I expect a small portion (less than 5%) to need a k bigger than 2. If the k values are mostly multiples of 6, that might allow us to refine Joshua's analysis below. If the gaps sizes need to be small for large k, there might be a good correlation. I expect gap size to drop as k gets large, but even knowing gap sizes by themselves without a correlation may point to a good conjecture. Gerhard "To Guess Where To Guess" Paseman, 2019.12.09. | |
| Dec 10, 2019 at 5:22 | comment | added | Space | @GerhardPaseman I will have to rerun the code with these specific details. How exactly do you plan use this data since it takes about 1-2 days to reach $10^9$ so the run time is going to be a few days. | |
| Dec 10, 2019 at 1:54 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
added 2 characters in body
|
| Dec 9, 2019 at 15:13 | comment | added | Gerhard Paseman | @Nilotpal, can you compute and then post here counts of a) number of primes tested, b) number of primes p where 2p is not maximal in a prime gap, and c) a breakdown in two ways, both by the value of k needed for kp to be maximal for k bigger than 3, and that count, also by size of prime gap interval where kp is maximal? Gerhard "Is Curious About Distribution Shape" Paseman, 2019.12.09. | |
| Dec 9, 2019 at 3:05 | comment | added | Nilotpal Kanti Sinha | @GerryMyerson For $59$ we have to go all the way up to the gap between the primes $59*18-1 =1061$ and $59*18+1 = 1063$. The farthest multiple of $p$ we have to go for any prime $p \le 3 \times 10^9$ is for $p = 2739366569$ where we need to go all the way up to $819$ times $p$. | |
| Dec 9, 2019 at 2:24 | answer | added | JoshuaZ | timeline score: 10 | |
| Dec 9, 2019 at 2:20 | comment | added | Gerry Myerson | @Sylvain if $p$ is a prime such that the next prime, $q$, after $2p$ is smaller than twice the next prime after $p$, then $p$ is the largest prime factor in the gap between $q$ and the prime previous to $q$. This is the case for many primes, in particular, for all primes through $p=53$. This may explain what you've seen. But for $p=59$, the next prime after $2p=118$ is $127$, which exceeds $2\times61=122$, so we have to go farther, in fact, quite a bit farther, to find the gap for $59$. And it's unlikely that $59$ disproves RH. | |
| Dec 9, 2019 at 2:00 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
deleted 2 characters in body
|
| Dec 8, 2019 at 17:27 | comment | added | Sylvain JULIEN | The first occurrence of a given prime $p$ in the oeis sequence seems to be at position $r$ such that $\sqrt{r}\log^2 r\approx p$. Maybe a connection with RH is possible. | |
| Dec 8, 2019 at 14:41 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
added 2 characters in body
|
| Dec 8, 2019 at 8:16 | comment | added | R Hahn | oeis.org/A052248 | |
| Dec 8, 2019 at 4:35 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
added 8 characters in body
|
| Dec 7, 2019 at 19:11 | history | edited | Pietro Majer | CC BY-SA 4.0 |
grammar
|
| Dec 7, 2019 at 18:07 | comment | added | Stanley Yao Xiao | I think either a proof or disproof is well beyond what we know how to do, so as stated the problem is more or less unanswerable. | |
| Dec 7, 2019 at 16:05 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
edited title
|
| Dec 7, 2019 at 13:31 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
added 96 characters in body
|
| Dec 7, 2019 at 8:46 | history | edited | Nilotpal Kanti Sinha | CC BY-SA 4.0 |
added 75 characters in body
|
| Dec 7, 2019 at 8:41 | history | asked | Nilotpal Kanti Sinha | CC BY-SA 4.0 |