A022547 Initial members of prime nonuplets (p, p+4, p+6, p+10, p+16, p+18, p+24, p+28, p+30).

13, 113143, 626927443, 2335215973, 3447123283, 4086982633, 4422726013, 6318867403, 7093284043, 8541306853, 10998082213, 14005112893, 18869466373, 21528117883, 21843411823, 28156779793, 30303283243

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn

Comments

All terms are congruent to 13 (modulo 30). - Matt C. Anderson, May 28 2015

Links

• Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 1000 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, 4, 6, 10, 16, 18, 24, 28, 30, zip archive.

Crossrefs

Cf. A022545, A022546, A022548.

Programs

Magma

[p: p in PrimesUpTo(2*10^8) | forall{p+r: r in [4,6,10,16,18,24,28,30] | IsPrime(p+r)}]; // Vincenzo Librandi, Sep 30 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:
# A prime constellation pattern of length 9
p := [0, 4, 6, 10, 16, 18, 24, 28, 30];
# using isprime(m*n+o+p)
o := [1273, 2263, 2683, 4003, 4633, 4993, 5893, 6883, 6943, 8623, 9613, 10243, 11563, 12823, 14863, 15133, 15553, 17863, 18433, 19753, 21163, 21793, 22483, 23053, 23113, 24103, 25783, 27733, 28723, 29983]:
with(ArrayTools):
os := Size(o, 2):
m := 30030:
loopstop := 10^11:
loopstart := 0:
print(13);
for n from loopstart to loopstop do
for a from 1 to os do
counter := 0; wc := 0; wd := 0;
while `and`(wd > -10, wd < 9) do
wd := wd+1;
if composite_small(m*n+o[a]+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[a]+p[wc]) then counter := counter+1 else counter := -1 end if;
end do;
end if;
if counter = 9 then print(m*n+o[a]) end if;
end do:
end do:
# Matt C. Anderson, Feb 01 2014

Mathematica

Select[Prime[Range[200000]], Union[PrimeQ[# + {4, 6, 10, 16, 18, 24, 28, 30}]] == {True} &] (* Vincenzo Librandi, Sep 30 2015 *)

PARI

forprime(p=2, 10^30, if (isprime(p+4) && isprime(p+6) && isprime(p+10) && isprime(p+16) && isprime(p+18) && isprime(p+24) && isprime(p+28) && isprime(p+30), print1(p", "))) \\ Altug Alkan, Sep 30 2015

Perl

use ntheory ":all"; say for sieve_prime_cluster(1,1e11, 4,6,10,16,18,24,28,30); # Dana Jacobsen, Sep 30 2015