%I #9 Feb 14 2018 17:56:33
%S 4094999,9080189,10957169,11148899,15917579,19422059,37267229,
%T 37622339,58680929,63196349,64595369,66383519,108463739,177109379,
%U 186977699,189997079,196068179,228875849,251891639,261703889,271031669,310143959
%N Primes p such that 2p+1, 4p+3, 6p+5, 8p+7, 10p+9, 12p+11 are all primes.
%H Donovan Johnson, <a href="/A107023/b107023.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%t 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
%t 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 *)
%Y 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).
%Y Cf. A005384, A007700, A107020, A107021, A107022, A107024.
%K nonn
%O 1,1
%A _Zak Seidov_, May 09 2005, Mar 08 2007