[math-fun] A091178: consecutive integers
https://oeis.org/A091178 Are there 100 (even more) consecutive integers? thx, zak
Yes. For example, take 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101. —Dan
On Aug 31, 2016, at 8:11 PM, Zak Seidov via math-fun <math-fun@mailman.xmission.com> wrote:
https://oeis.org/A091178 Are there 100 (even more) consecutive integers?
On 8/31/2016 11:11 PM, Zak Seidov via math-fun wrote:
(i.e., the sequence of integers n for which the nth prime is 1 mod 6)
Are there 100 (even more) consecutive integers?
Yes. This is a special case of Daniel Shiu's theorem that every (admissible) congruence class contains arbitrarily long strings of consecutive primes ("Strings of congruent primes", J. London Math. Soc. (2000) 61 (2): 359-373). It's a very powerful theorem that deserves to be better known. -- Fred W. Helenius fredh@ix.netcom.com
Yes, I know (about) DST, but are there 100 (even more) consecutive integers in: https://oeis.org/A091178 Right now the maximal known number is 35(?): https://oeis.org/A057620
Четверг, 1 сентября 2016, 7:19 +03:00 от "Fred W. Helenius" <fredh@ix.netcom.com>:
On 8/31/2016 11:11 PM, Zak Seidov via math-fun wrote:
(i.e., the sequence of integers n for which the nth prime is 1 mod 6)
Are there 100 (even more) consecutive integers?
Yes. This is a special case of Daniel Shiu's theorem that every (admissible) congruence class contains arbitrarily long strings of consecutive primes ("Strings of congruent primes", J. London Math. Soc. (2000) 61 (2): 359-373). It's a very powerful theorem that deserves to be better known.
-- Fred W. Helenius fredh@ix.netcom.com
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participants (3)
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Dan Asimov -
Fred W. Helenius -
Zak Seidov