%I
%S 1973,3769,7727,11903,14629,16903,17737,18097,19477,20747,20759,21727,
%T 22717,23567,25037,27397,27529,28279,29207,29959,30497,31319,33289,
%U 36097,37463,42139,42487,42689,45959,46229,47309,47969,48847,48947
%N Prime numbers p not of the form 10k+1 for which the quintic polynomial x^5x1 modulus p is factorizable into five binomials.
%C This sequence is a subsequence of A135844.
%H Robert Israel, <a href="/A135845/b135845.txt">Table of n, a(n) for n = 1..10000</a>
%p filter:= proc(p) isprime(p) and nops([msolve(x^5x1,p)])=5 end proc:
%p select(filter, [seq(seq(10*k+j,j=[3,7,9]),k=0..10000)]); # _Robert Israel_, Jul 03 2018
%t a = {}; Do[If[Mod[Prime[n], 1, poly = PolynomialMod[x^5  x  1, Prime[n]]; c = FactorList[poly, Modulus > Prime[n]]; If[Sum[c[[m]][[2]], {m, 1, Length[c]}] == 6, AppendTo[a, Prime[n]]]], {n, 1, 10000}]; a
%Y Cf. A135842, A135843, A135844, A135846, A135847.
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 01 2007
