31 Aug
2016
31 Aug
'16
10:20 p.m.
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