A057631 Initial prime in first sequence of n primes congruent to 3 modulo 5.

3, 283, 6793, 22963, 752023, 2707163, 44923183, 44923183, 961129823, 1147752443, 6879806623, 131145172583, 177746482483, 795537219143, 4028596340953, 6987191424553, 269013937530553, 281659318133953, 281659318133953

Offset: 1

Author

Robert G. Wilson v, Oct 10 2000

Keywords

• nonn

Examples

			a(6) = 2707163 because this number is the first in a sequence of 6 consecutive primes all of the form 5n + 3.
		

Links

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

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 ] != {3}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 5 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 9} ]

Extensions

a(10) from Jud McCranie, Jan 14 2003

More terms from Jens Kruse Andersen, Jun 03 2006

a(17)-a(19) from Giovanni Resta, Aug 04 2013