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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). 33
9853497737, 21956291867, 22741837817, 164444511587, 179590045487, 217999764107, 231255798857, 242360943257, 666413245007, 696391309697, 867132039857, 974275568237, 976136848847, 1002263588297, 1086344116367 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 by Matt C. Anderson]

T. Forbes, Prime k-tuplets

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

PROG

(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

CROSSREFS

Sequence in context: A256622 A022251 A015385 * A202362 A204058 A154532

Adjacent sequences:  A027567 A027568 A027569 * A027571 A027572 A027573

KEYWORD

nonn

AUTHOR

Warut Roonguthai

STATUS

approved

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Last modified December 3 21:14 EST 2016. Contains 278745 sequences.