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

Author

Zak Seidov, May 09 2005, Mar 08 2007

Keywords

• nonn

Examples

			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.
		

Links

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

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.

Programs

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 *)