A137463 Prime numbers p such that p^3 - p + 1 and p^3 + p - 1 are both primes.

7, 139, 631, 739, 769, 991, 1201, 1231, 2677, 3499, 3931, 4261, 4441, 4861, 6247, 7411, 7699, 8377, 9391, 10711, 10837, 14389, 15139, 15679, 16057, 16561, 18541, 20479, 22861, 28111, 28837, 29917, 30169, 30367, 32089, 33589, 35311, 35677

Offset

1,1

Links

Table of n, a(n) for n=1..38.

Example

7^3 +- 6 -> (337, 349) (both primes),
139^3 +- 138 -> (2685481, 2685757) (both primes).

Maple

a:=proc (n) if isprime(n)=true and isprime(n^3+n-1)=true and isprime(n^3-n+1) =true then n else end if end proc: seq(a(n), n=1..30000); # Emeric Deutsch, Apr 29 2008

Mathematica

Select[Prime[Range[900]], PrimeQ[ #^3-(#-1)]&&PrimeQ[ #^3+(#-1)]&]

Prog

(Magma) [ n: n in [0..40000] | IsPrime(n) and IsPrime(n^3-(n-1)) and IsPrime(n^3 +(n-1)) ]; // Vincenzo Librandi, Nov 24 2010

Crossrefs

Sequence in context: A217504 A142295 A056254 * A274525 A221375 A351334

Adjacent sequences: A137460 A137461 A137462 * A137464 A137465 A137466

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2008

Extensions

More terms from Emeric Deutsch, Apr 29 2008

Status

approved