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

Author

Jason Earls, Jul 02 2001

Keywords

• nonn
• easy

Comments

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

Examples

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

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

Crossrefs

Cf. A062288.

Programs

Magma

[p: p in PrimesUpTo(2000) | IsPrime(p+50)]; // Vincenzo Librandi, Apr 22 2015

Mathematica

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

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

Extensions

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