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A022548 Initial members of prime nonuplets (p, p+4, p+10, p+12, p+18, p+22, p+24, p+28, p+30). 30
88789, 855709, 74266249, 964669609, 1422475909, 2117861719, 2558211559, 2873599429, 5766036949, 6568530949, 8076004609, 9853497739, 16394542249, 21171795079, 21956291869, 22741837819, 26486447149, 27254489389 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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]

T. Forbes, Prime k-tuplets

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 *)

PROG

(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e11, 4, 10, 12, 18, 22, 24, 28, 30); # Dana Jacobsen, 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

CROSSREFS

Sequence in context: A233937 A022201 A031857 * A022013 A233038 A205835

Adjacent sequences:  A022545 A022546 A022547 * A022549 A022550 A022551

KEYWORD

nonn

AUTHOR

Warut Roonguthai

STATUS

approved

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Last modified April 25 00:29 EDT 2019. Contains 322446 sequences. (Running on oeis4.)