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A233540
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Primes p such that p+2, p+8, and p+12 are all prime.
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2
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5, 11, 29, 59, 71, 101, 269, 431, 1289, 1481, 2129, 2339, 2381, 2789, 4721, 5519, 5639, 5849, 6569, 6959, 8999, 10091, 13679, 14549, 16061, 16649, 16691, 18119, 19379, 19421, 19751, 21011, 21491, 22271, 25931, 27689, 27791, 28619, 31181, 32369, 32561, 32831
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OFFSET
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1,1
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COMMENTS
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The primes produced (p, p+2, p+8, p+12) are not always consecutive primes.
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LINKS
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FORMULA
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EXAMPLE
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29 is in the sequence because 29, 29 + 2 = 31, 29 + 8 = 37, and 29 + 12 = 41 are all prime.
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MAPLE
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KD := proc() local a, b, c, p; p:=ithprime(n); a:=p+2; b:=p+8; c:=p+12; if isprime(a)and isprime(b) and isprime(c) then RETURN (p); fi; end: seq(KD(), n=1..10000);
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MATHEMATICA
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Select[Prime[Range[4000]], AllTrue[#+{2, 8, 12}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 04 2016 *)
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PROG
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(PARI) is_a233540(p) = isprime(p) && isprime(p+2) && isprime(p+8) && isprime(p+12) \\ Michael B. Porter, Dec 27 2013
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CROSSREFS
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Cf. A078848 (same prime differences, but with consecutive primes).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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