A263311 Numbers n such that each of p=6*n+1, q=6*p+1, r=6*q+1 and s=6*r+1 is prime.

10, 1060, 1795, 1885, 2965, 3245, 3335, 4065, 4325, 5015, 5875, 6985, 7605, 7905, 9785, 11315, 12045, 12360, 14390, 14970, 15285, 15500, 15885, 17195, 18220, 20670, 20695, 22160, 24915, 25645, 25955, 26025, 29410, 29910, 32925, 35530, 36280

Offset: 1

Author

Zak Seidov, Oct 13 2015

Keywords

• nonn

Comments

Each p is a starting prime of a complete generalized Cunningham chain p(k)=6*p(k-1)+1.

All terms are multiples of 5. Hence t = 6s+1 = 1555+7776n are always composite, and the chains are indeed "complete."

Subsequence of A263310 (and as such of A263309 and of A024899).

Links

• Zak Seidov, Table of n, a(n) for n = 1..20000
• Wikipedia, Cunningham chain

Crossrefs

Cf. A024899, A263309, A263310.

Programs

Maple

isA263311 := proc(n)
    return isprime(6*n+1) and isprime(36*n+7) and isprime(216*n+43) and isprime(1296*n+259) ;
end proc:
for n from 1 to 30000 do
    if isA263311(n) then
        printf("%d,",n);
    end if;
end do; # R. J. Mathar, Oct 17 2015

Mathematica

Select[Range[10,100000,5],PrimeQ[p=6*#+1]&&PrimeQ[q=6*p+1]&&PrimeQ[r=6*q+1]&&PrimeQ[s=6*r+1]&]

PARI

for(n=1, 1e5, if(isprime(p=6*n+1) && isprime(q=6*p+1) && isprime(r=6*q+1) && isprime(6*r+1), print1(n", "))) \\ Altug Alkan, Oct 17 2015