A055625 First prime starting a chain of exactly n consecutive primes congruent to 1 modulo 6.

7, 31, 151, 3049, 7351, 1741, 19471, 118801, 498259, 148531, 406951, 2513803, 2339041, 89089369, 51662593, 73451737, 232301497, 450988159, 1558562197, 2506152301, 1444257673, 28265029657, 24061965043, 87996684091, 43553959717

Offset: 1

Author

Labos Elemer, Jun 05 2000

Keywords

• nonn

Comments

The term "exactly" means that before the first and after the last primes of chain, the immediate primes are not congruent to 1 modulo 6.

See A057620 for the variant where "exactly" is replaced by "at least". - M. F. Hasler, Sep 03 2016

Links

• Giovanni Resta, Table of n, a(n) for n = 1..35 (terms < 4*10^14)
• J. K. Andersen, Consecutive Congruent Primes.
• A. Granville and G. Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

Crossrefs

Cf. A055623, A055624, A055626, A085515.

Programs

Fortran

c See link in A085515.

Mathematica

pp = Table[{p = Prime[n], Mod[p, 6]}, {n, 10^6}];
sp = Split[pp, Mod[#1[[2]], 6] == Mod[#2[[2]], 6]&];
a[n_] := SelectFirst[sp, Length[#] == n && MatchQ[#, {{_Integer, 1} ..}]& ][[1, 1]];
Table[an = a[n]; Print[n, " ", an]; an, {n, 1, 13}] (* Jean-François Alcover, Nov 21 2018 *)

Extensions

Corrected and extended by Reiner Martin, May 19 2001

More terms from Hugo Pfoertner, Jul 31 2003

a(20)>2^31, a(21)=1444257673. - Hugo Pfoertner, Jul 31 2003

More terms from Jens Kruse Andersen, May 30 2006

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 27 2006