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%I #23 Sep 08 2022 08:45:03
%S 3,11,17,23,29,47,53,59,89,101,107,113,131,149,173,179,191,227,233,
%T 257,263,281,317,347,359,383,389,449,491,521,557,563,569,593,641,659,
%U 677,683,701,719,761,773,809,827,857,887,941,947,971,983,1013,1019,1103
%N Primes p such that p + 50 is also prime.
%C "Numerical evidence makes it plausible that there are infinitely many primes p such that p + 50 is also prime", see Burton in References.
%D D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc., Boston, MA, 1976, p. 52.
%H Harry J. Smith, <a href="/A062284/b062284.txt">Table of n, a(n) for n = 1..1000</a>
%e a(3)=17 since 17+50= 67, a prime.
%t Select[Range[2000], PrimeQ[#] && PrimeQ[# + 50] &] (* _Vincenzo Librandi_, Apr 22 2015 *)
%t Select[Prime[Range[200]],PrimeQ[#+50]&] (* _Harvey P. Dale_, Jun 17 2020 *)
%o (PARI) for(n=1,60, if(isprime(prime(n)+50),print(prime(n))))
%o (PARI) { n=0; forprime (p=2, 10^5, if (isprime(p + 50), write("b062284.txt", n++, " ", p); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 04 2009
%o (Magma) [p: p in PrimesUpTo(2000) | IsPrime(p+50)]; // _Vincenzo Librandi_, Apr 22 2015
%Y Cf. A062288.
%K nonn,easy
%O 1,1
%A _Jason Earls_, Jul 02 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), Jul 05 2001
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