A062284 Primes p such that p + 50 is also prime.

3, 11, 17, 23, 29, 47, 53, 59, 89, 101, 107, 113, 131, 149, 173, 179, 191, 227, 233, 257, 263, 281, 317, 347, 359, 383, 389, 449, 491, 521, 557, 563, 569, 593, 641, 659, 677, 683, 701, 719, 761, 773, 809, 827, 857, 887, 941, 947, 971, 983, 1013, 1019, 1103

Offset

1,1

Comments

"Numerical evidence makes it plausible that there are infinitely many primes p such that p + 50 is also prime", see Burton in References.

References

D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc., Boston, MA, 1976, p. 52.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

a(3)=17 since 17+50= 67, a prime.

Mathematica

Select[Range[2000], PrimeQ[#] && PrimeQ[# + 50] &] (* Vincenzo Librandi, Apr 22 2015 *)
Select[Prime[Range[200]], PrimeQ[#+50]&] (* Harvey P. Dale, Jun 17 2020 *)

Prog

(PARI) for(n=1, 60, if(isprime(prime(n)+50), print(prime(n))))
(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
(Magma) [p: p in PrimesUpTo(2000) | IsPrime(p+50)]; // Vincenzo Librandi, Apr 22 2015

Crossrefs

Cf. A062288.

Sequence in context: A075334 A056983 A175073 * A141339 A069348 A165561

Adjacent sequences: A062281 A062282 A062283 * A062285 A062286 A062287

Keyword

nonn,easy

Author

Jason Earls, Jul 02 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jul 05 2001

Status

approved