A022546 Initial members of prime nonuplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26, p+30).

17, 1277, 113147, 252277007, 408936947, 521481197, 1116452627, 1209950867, 1645175087, 2966003057, 3947480417, 6234613727, 9307040837, 9853497737, 11878692167, 13766391467, 21956291867, 22741837817, 24388061207

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn

Comments

Subsequence of A022012. - R. J. Mathar, Feb 10 2013

All terms congruent to 17 (modulo 30). - Matt C. Anderson, May 27 2015

Links

• Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 200 terms from Matt C. Anderson]
• Tony Forbes and Norman Luhn, Prime k-tuplets
• Norman Luhn, The first 10^6 initial members of prime 9-tuplets | pattern: d= 0, 2, 6, 12, 14, 20, 24, 26, 30, zip archive.

Crossrefs

Cf. A022545, A022547, A022548.

Programs

Magma

[p: p in PrimesUpTo(260000000) | forall{p+r: r in [2, 6, 12,14,20,24,26,30] | IsPrime(p+r)}]; // Vincenzo Librandi, May 27 2015

Maple

composite_small := proc (n::integer)
description "determine if n has a prime factor less than 100";
if igcd(2305567963945518424753102147331756070, n) = 1 then return false else return true;
end if ;
end proc:
p := [0, 2, 6, 12, 14, 20, 24, 26, 30]:
# using isprime(m*n+o+p)
o := 17:
m:=30:
loopstop:=10^11:
loopstart:=0:
for n from loopstart to loopstop do
counter := 0:
wc := 0;
wd := 0;
while `and`(wd > -10, wd < 9) do
wd := wd+1;
if composite_small(m*n+o+p[wd]) = false then wd := wd+1 else wd := -10 end if ;
end do;
if wd >= 9 then
while `and`(counter >= 0, wc < 9) do
wc := wc+1;
if isprime(m*n+o+p[wc]) then counter := counter+1 else counter := -1 end if;
end do end if;
if counter = 9 then print(m*n+o) end if;
end do:

Mathematica

Select[Prime[Range[260000000]], Union[PrimeQ[ # +{2, 6, 12, 14, 20, 24, 26, 30}]]=={True} &] (* Vincenzo Librandi, May 27 2015 *)

PARI

forprime(p=2, 1e30, if (isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+14) && isprime(p+20) && isprime(p+24) && isprime(p+26) && isprime(p+30) , print1(p", "))) \\ Altug Alkan, Sep 30 2015

Perl

use ntheory ":all"; say for sieve_prime_cluster(1,1e11, 2,6,12,14,20,24,26,30); # Dana Jacobsen, Sep 30 2015