A022010 - OEIS (original) (raw)

5639, 88799, 284729, 626609, 855719, 1146779, 6560999, 7540439, 8573429, 17843459, 19089599, 24001709, 42981929, 43534019, 69156539, 74266259, 79208399, 80427029, 84104549, 87988709, 124066079, 128469149, 144214319, 157131419, 208729049, 218033729

COMMENTS

All terms are congruent to 179 (modulo 210). - Matt C. Anderson, May 26 2015

EXAMPLE

a(100) = 2526962939, a(1000) = 80752495919, a(10000) = 2010407120789, a(100000) = 42609827234069, a(1000000) = 822249634821059. See illustration for asymptotic behavior. - Hugo Pfoertner, Jun 15 2020

MATHEMATICA

Select[Prime[Range[2 10^8]], Union[PrimeQ[# + {2, 8, 12, 14, 18, 20}]] == {True} &] (* Vincenzo Librandi, Oct 01 2015 *)

Select[Partition[Prime[Range[12021000]], 7, 1], Differences[#]=={2, 6, 4, 2, 4, 2}&][[All, 1]] (* or *) Select[Range[179, 219*10^6, 210], AllTrue[ #+{0, 2, 8, 12, 14, 18, 20}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 04 2019 *)

PROG

(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e9, 2, 8, 12, 14, 18, 20); # Dana Jacobsen, Sep 30 2015

(Magma) [p: p in PrimesUpTo(3*10^8) | forall{p+r: r in [2, 8, 12, 14, 18, 20] | IsPrime(p+r)}]; // Vincenzo Librandi, Oct 01 2015

(PARI) forprime(p=2, 10^30, if (isprime(p+2) && isprime(p+8) && isprime(p+12) && isprime(p+14) && isprime(p+18) && isprime(p+20), print1(p", "))) \\ Altug Alkan, Oct 01 2015. [This can be made 2x faster by inserting "p%210==179 &&" before or after "if(". - M. F. Hasler, Aug 04 2021]