Timeline for question in prime numbers
Current License: CC BY-SA 2.5
17 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Sep 7, 2015 at 14:23 | comment | added | Brad Graham | @Gerhard We can make more natural statements from the p_n * log(log(log(p_n))) result, such as there exists no sequence of integers which are consecutive and not coprime to the nth primorial, with a length of $p_n^2$ | |
| Dec 22, 2010 at 16:43 | vote | accept | Asterios Gkantzounis | ||
| Dec 22, 2010 at 16:43 | |||||
| Dec 14, 2010 at 23:07 | comment | added | Asterios Gkantzounis | thnx very much and i am waiting for results from your research. is there any in english? | |
| Dec 14, 2010 at 22:58 | comment | added | Gerhard Paseman | Oh. The question I linked to had the citation (thanks to Pete Clark for moving it to the top of the linked question.) Here it is: Ueber die Verteilung der Zahlen, die zu den n ersten Primzahlen teilerfremd sind, Comm. Phys. Math. Soc. Sci. Fenn., Helsingfors (5) 25 (1931), 1-37 Later I may provide a summary of the argument, but I am still working through his paper. Gerhard "Ask Me About System Design" Paseman, 2010.12.14 | |
| Dec 14, 2010 at 22:45 | comment | added | Asterios Gkantzounis | i didnt mean to write in capitals | |
| Dec 14, 2010 at 22:44 | comment | added | Asterios Gkantzounis | I MEAN IF YOU CAN TELL ME WHERE I CAN FIND A PROOF OF WASTZYNTHIOUS RESULT | |
| Dec 14, 2010 at 22:24 | comment | added | Gerhard Paseman | Briefly then: By Westzynthius's result, there is an n (in fact infinitely many different n) such that S(n) has gaps larger than p_n * log(log(log(p_n))) Pick n such that this quantity is 3*p_n. Then there is a sequence of integers which is consecutive, contains at least 3*p_n integers, and none of them are relatively prime to the nth primorial. (If one of these were, we could not find such a gap in S(n) ). As n is large enough this contains a sequence of 2*p_n numbers none of which has all its factors greater than p_n. Gerhard "Hope That Clears It Up" Paseman, 2010.12.14 | |
| Dec 14, 2010 at 22:02 | comment | added | Asterios Gkantzounis | yes of the claims that you have post above i want to see a proof. | |
| Dec 14, 2010 at 21:59 | comment | added | Gerhard Paseman | Of my research, I am still doing the writing; of the claims in my post above, I do not understand. Of what part do you wish to have an exact proof? Gerhard Paseman, 2010.12.14 | |
| Dec 14, 2010 at 20:44 | comment | added | Asterios Gkantzounis | i want an exact proof of what you have stated pls | |
| Dec 14, 2010 at 19:07 | comment | added | Asterios Gkantzounis | i would like to read carefully your research | |
| Dec 14, 2010 at 18:54 | comment | added | Gerhard Paseman | Yes. In addition to my own research (still under development but you can be added to the list of reviewers), there is research on prime gaps by Erdos, Rankin, and others. Hans Riesel has a book "Prime numbers and computer methods for factorization" which has a readable account of this as well as admissible constellations, which is related to your question. Marek Wolf and others have also done related work. A search for "prime gaps" will get you started. Gerhard "Ask Me About System Design" Paseman, 2010.12.14 | |
| Dec 14, 2010 at 18:44 | comment | added | Asterios Gkantzounis | do you have any other information about this kind of questions or Westzynthius proof? | |
| Dec 14, 2010 at 18:25 | comment | added | Gerhard Paseman | I do too. If you have computing power (and a lot of memory) available to you, here are two programs you can build and run: the first computes S(n) or the largest gap in S(n), which is easy for small n; the second starts with the largest untried n from the first program and searches through the table of smallest factors of natural numbers for long runs of small factors. A good place to look for such runs are intervals centered on (P_n)/2, with P_n being the nth primorial. Gerhard "Ask Me About System Design" Paseman, 2010.12.14 | |
| Dec 14, 2010 at 18:12 | comment | added | Asterios Gkantzounis | i want to know about when a sequence of length 2*p_n consecutive numbers all of which have a factor among the first n-1 primes | |
| Dec 14, 2010 at 17:25 | history | answered | Gerhard Paseman | CC BY-SA 2.5 |