A236688 Primes p such that prime(p^2) + 2 is also prime.
7, 53, 83, 107, 149, 223, 367, 509, 701, 769, 853, 971, 1039, 1229, 1283, 1327, 1373, 1381, 1439, 1447, 1459, 1783, 1873, 1973, 2237, 2243, 2269, 2339, 2347, 2437, 2459, 2521, 2531, 2797, 2857, 3001, 3391, 3413, 3461, 3583, 3593, 3631, 3659, 3769, 3889, 3947
Offset: 1
Keywords
Examples
7 is prime and appears in the sequence: prime(7^2) = 227 and 227+2 = 229, which is also prime. 53 is prime and appears in the sequence: prime(53^2) = 25469 and 25469+2 = 25471, which is also prime.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..1119
Programs
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Maple
KD := proc() local a,b; a:=ithprime(n); b:=ithprime(a^2)+2; if isprime (b) then RETURN (a);fi; end: seq(KD(), n=1..700);
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Mathematica
Select[Prime[Range[600]],PrimeQ[Prime[#^2]+2]&] (* Harvey P. Dale, Aug 29 2021 *)
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PARI
default(primelimit,2^31) s=[]; forprime(p=2, 4000, if(isprime(prime(p^2)+2), s=concat(s, p))); s \\ Colin Barker, Jan 30 2014