

A274465


Primes which are the sum of cousin prime pairs  1.


1



17, 29, 41, 89, 137, 197, 257, 389, 449, 461, 557, 617, 701, 761, 797, 881, 929, 977, 1229, 1289, 1481, 1709, 1721, 1877, 2609, 2861, 2897, 2969, 3137, 3221, 3329, 3389, 3989, 4001, 4409, 4481, 4877, 5081, 5237, 5381, 5417, 5501, 5669, 5717, 6329, 6689, 6917, 7229
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OFFSET

1,1


COMMENTS

Cousin primes are prime pairs that differ by 4. Any prime p in this sequence is such that p = (p3)/2 + (p+5)/2  1, where (p3)/2 and (p+5)/2 are also primes and they differ by 4.


LINKS



EXAMPLE

17 = 7 + 11  1. Note that, (173)/2 = 7 and (17+5)/2 = 11 and 7, 11 are cousin prime pairs.
29 = 13 + 17  1. Note that, (293)/2 = 13 and (29+5)/2 = 17 and 13, 17 are cousin prime pairs.
41 = 19 + 23  1. Note that, (413)/2 = 19 and (41+5)/2 = 23 and 19, 23 are cousin prime pairs.
89 = 43 + 47  1. Note that, (893)/2 = 43 and (89+5)/2 = 47 and 43, 47 are cousin prime pairs.


MATHEMATICA

Select[2 # + 3 &@ Select[Prime@ Range@ 512, PrimeQ[# + 4] &], PrimeQ] (* Michael De Vlieger, Jun 26 2016 *)


PROG

(PARI) is(n) = isprime(n) && isprime((n3)/2) && isprime((n+5)/2) \\ David A. Corneth, Jun 24 2016
(Perl) use ntheory ":all"; say for grep{is_prime($_)} map { $_+$_+41 } sieve_prime_cluster(1, 5e8, 4) # Dana Jacobsen, Apr 27 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



