Timeline for On hashing prime numbers into prime number of buckets
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 28 at 14:33 | history | edited | Nandakumar R | CC BY-SA 4.0 |
added 4 characters in body
|
| Mar 23 at 11:08 | history | edited | Nandakumar R | CC BY-SA 4.0 |
added 271 characters in body
|
| Mar 22 at 10:37 | comment | added | Nandakumar R | thank you again. what i gather from the conjecture is: if we allow N to be large enough, the number of entries in the 6 buckets will equalize even when we hash only those primes immediately following primes which give remainder 3 modulo 7(say). numerically, i could go up to N = 100 million and there is no clear indication that they do. but then, if N gets really large, things could be different. One can always ask for other hash functions for which one doesn't have to wait as long. | |
| Mar 22 at 0:29 | comment | added | Gerry Myerson | Doesn't the paper of Oliver and Soundararajan answer question 3, at least conjecturally? "...we predict that all patterns do occur their fair share of the time in the limit...." | |
| Mar 21 at 9:55 | history | edited | Nandakumar R | CC BY-SA 4.0 |
added 183 characters in body
|
| Mar 21 at 9:51 | comment | added | Nandakumar R | Thanks to Padraig O'Cathain, Michael Hardy and Gerry Myerson. From these comments, questions 1 has a ready answer and 2 is discussed in the paper by Oliver and Soundararajan. That leaves question 3. | |
| Mar 21 at 6:07 | comment | added | Gerry Myerson | The paper is discussed at mathoverflow.net/questions/233633/… and mathoverflow.net/questions/357379/… and mathoverflow.net/questions/372572/… and mathoverflow.net/questions/234108/… and several other places on this website. | |
| Mar 21 at 6:03 | comment | added | Gerry Myerson | Prime numbers ... are well known to be very well distributed among the reduced residue classes $\bmod q$. Surprisingly, the same does not appear to be true for sequences of consecutive primes, with different patterns occurring with wildly different frequencies. We formulate a precise conjecture, based on the Hardy−Littlewood conjectures, which explains this phenomenon. In particular, we predict that all patterns do occur their fair share of the time in the limit, but that there are secondary terms only very slowly tending to zero that create the observed biases. | |
| Mar 21 at 6:00 | comment | added | Gerry Myerson | As for the question of dependence of a prime on the previous prime, see Robert J Lemke Oliver and Kannan Soundararajan, Unexpected biases in the distribution of consecutive primes, Proc Nat Acad Sci 113 #31 (2016) E4446-E4454, available at pnas.org/doi/full/10.1073/pnas.1605366113. Abstract next comment. | |
| Mar 20 at 19:21 | comment | added | Michael Hardy | Writing $b$-1 instead of $b-1$ is definitely incorrect usage in MathJax or LaTeX. That has been edited above. | |
| S Mar 20 at 19:20 | history | edited | Michael Hardy | CC BY-SA 4.0 |
some MathJax improvements
|
| S Mar 20 at 19:20 | history | suggested | Marco Ripà | CC BY-SA 4.0 |
Minor edit, just rearranging some $$
|
| Mar 20 at 18:56 | review | Suggested edits | |||
| S Mar 20 at 19:20 | |||||
| Mar 20 at 18:50 | comment | added | Padraig Ó Catháin | Granville and Martin wrote a paper where this is discussed: arxiv.org/pdf/math/0408319.pdf They explain many details of the behaviour of these 'prime races'. Some buckets are fuller than others most of the time, as you have observed. They can quantify by how much some buckets lead, and how often. The tie all this to the Riemann hypothesis - it's a really nice paper. | |
| Mar 20 at 17:44 | history | asked | Nandakumar R | CC BY-SA 4.0 |