A107023 Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 are all primes.

4094999, 9080189, 10957169, 11148899, 15917579, 19422059, 37267229, 37622339, 58680929, 63196349, 64595369, 66383519, 108463739, 177109379, 186977699, 189997079, 196068179, 228875849, 251891639, 261703889, 271031669, 310143959

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

a(1) = p = 4094999 is a term because numbers i*p+(i-1), i=2(2)12 8189999,16379999,24569999,32759999,40949999,49139999 are all primes.

Mathematica

s={}; Do[p=Prime[i]; If[Union[PrimeQ[Table[i*p+(i-1), {i, 2, 12, 2}]]]=={True}, AppendTo[s, p]], {i, 289435, 1236230}]; s
With[{t=Table[2n #+(2n-1), {n, 6}]}, Select[Prime[ Range[ 168*10^5]], AllTrue[ t, PrimeQ]&]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 14 2018 *)

Crossrefs

Cf. A107024: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11, 14p+13 all prime; A107022: p, 2p+1, 4p+3, 6p+5, 8p+7, 10p+9 all prime; A107021: p, 2p+1, 4p+3, 6p+5, 8p+7 all prime;A107020: p, 2p+1, 4p+3, 6p+5 all prime; A007700: p, 2p+1, 4p+3 all prime; A005384: p, 2p+1 prime (p = Sophie Germain primes).

Cf. A005384, A007700, A107020, A107021, A107022, A107024.

Sequence in context: A191346 A307846 A278199 * A107024 A250862 A345615

Adjacent sequences: A107020 A107021 A107022 * A107024 A107025 A107026

Keyword

nonn

Author

Zak Seidov, May 09 2005, Mar 08 2007

Status

approved