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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