

A057631


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


2



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

1,1


REFERENCES

Carlos Rivera's The prime puzzles & problems connection, Puzzle 16  Consecutive primes and ending digit


LINKS

Table of n, a(n) for n=1..19.
J. K. Andersen, Consecutive Congruent Primes.


EXAMPLE

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


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} ]


CROSSREFS

Sequence in context: A239273 A054583 A139984 * A058455 A116532 A199644
Adjacent sequences: A057628 A057629 A057630 * A057632 A057633 A057634


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Oct 10 2000


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


STATUS

approved



