A057618 Initial prime in first sequence of n primes congruent to 1 modulo 5.

11, 181, 4831, 22501, 216401, 2229971, 3873011, 36539311, 36539311, 196943081, 14293856441, 154351758091, 154351758091, 154351758091, 11992377039481, 41947964349971, 253931039382791, 253931039382791, 253931039382791

Offset: 1

Author

Robert G. Wilson v, Oct 09 2000

Keywords

• nonn

Comments

a(20) > 4*10^14. - Giovanni Resta, Aug 04 2013

Examples

			a(6) = 2229971 because this number is the first in a sequence of 6 consecutive primes all of the form 5n + 1.
		

Links

• J. K. Andersen, Consecutive Congruent Primes.
• Carlos Rivera, Puzzle 16 - Consecutive primes and ending digit, The prime puzzles & problems connection.

Crossrefs

Cf. A054681.

Programs

Mathematica

NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ] ]; p = 0; Do[ a = Table[ -1, {n} ]; k = Max[ 1, p ]; While[ Union[ a ] != {1}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 5 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 10} ]

Extensions

More terms from Jens Kruse Andersen, Jun 03 2006

a(15)-a(19) from Giovanni Resta, Aug 04 2013