A022548 Initial members of prime nonuplets (p, p+4, p+10, p+12, p+18, p+22, p+24, p+28, p+30).

88789, 855709, 74266249, 964669609, 1422475909, 2117861719, 2558211559, 2873599429, 5766036949, 6568530949, 8076004609, 9853497739, 16394542249, 21171795079, 21956291869, 22741837819, 26486447149, 27254489389

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn

Comments

All terms are congruent to 169 (modulo 210). - Matt C. Anderson, May 28 2015

Links

• Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 800 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, 10, 12, 18, 22, 24, 28, 30, zip archive.

Crossrefs

Cf. A022545, A022546, A022547.

Programs

Maple

a := 1; for b to 25 do a := a*ithprime(b) end do; a;
# so ‘a’ is the product of the primes 2 through 97
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;
# my technique involves isprime(m*n+o+p)
# with Multiplier, Number, Offset, and Pattern
p := [0, 4, 10, 12, 18, 22, 24, 28, 30];
o := [2059, 6679, 7519, 8989, 10249, 12139, 14449, 14869, 15919, 17179, 20539, 21379, 24109, 25999, 28729];
with(ArrayTools);
os := Size(o, 2);
ps := Size(p, 2);
m := 30030;
loopstop := 10^11;
loopstart := 0;
for n from loopstart to loopstop do
for a to os do
counter := 0; wc := 0; wd := 0;
while `and`(wd > -10, wd < ps) 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 < ps) 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 = ps then print(m*n+o[a]) end if;
end do;
end do;
# Matt C. Anderson, Feb 13 2014

Mathematica

Select[Prime[Range[2 10^6]], Union[PrimeQ[# + {4, 10, 12, 18, 22, 24, 28, 30}]] == {True} &] (* Vincenzo Librandi, Sep 30 2015 *)

PARI

forprime(p=2, 10^30, if (isprime(p+4) && isprime(p+10) && isprime(p+12) && isprime(p+18) && isprime(p+22) && 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, 4,10,12,18,22,24,28,30); # Dana Jacobsen, Sep 30 2015