A027570 Initial members of prime decaplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26, p+30, p+32).

9853497737, 21956291867, 22741837817, 164444511587, 179590045487, 217999764107, 231255798857, 242360943257, 666413245007, 696391309697, 867132039857, 974275568237, 976136848847, 1002263588297, 1086344116367

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn

Comments

All terms are congruent to 167 (modulo 210). - Matt C. Anderson, May 29 2015

Links

• Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 100 terms from Matt C. Anderson]
• Tony Forbes and Norman Luhn, Prime k-tuplets
• Norman Luhn, 1 million terms of A027570, zip compressed (7.94 MB) (2021).

Crossrefs

Cf. A027569, A202361, A202362.

Programs

Maple

a := 1:
for b to 25 do
a := a*ithprime(b):
end do:
a;
# now 'a' is the product of the primes less than 100.
composite_small := proc (n::integer)
description "procedure to 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:
# so composite_small tests if there are any factors 2 through 97.
#begin initialization section
p := [0, 2, 6, 12, 14, 20, 24, 26, 30, 32];
o := [7517, 10247, 12137, 14447, 14867, 17177, 21377, 24107, 25997, 28727];
m := 30030;
#end initialization section
# implement isprime(m*n+o+p)
with(ArrayTools):
os:=Size(o,2):
ps:=Size(p,2):
#here ps is 10 so a prime constellation of length 10.
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, Apr 15 2015

Perl

use ntheory ":all"; say for sieve_prime_cluster(1,1e13, 2,6,12,14,20,24,26,30,32); # Dana Jacobsen, Sep 30 2015