A174409 Prime numbers p such that the concatenation p^3//1331 is a prime number.

2, 107, 137, 167, 257, 269, 311, 317, 557, 593, 761, 773, 809, 911, 1103, 1151, 1283, 1289, 1481, 1487, 1559, 1709, 1787, 1931, 2111, 2141, 2243, 2339, 2357, 2657, 2687, 2777, 2909, 3137, 3209, 3251, 3359, 3371, 3389, 3449

Offset

1,1

Comments

See comments at A174213.

p^3//1331 is the concatenation of the cubes of two primes.

With the exception of a(1)=2, each term is necessarily of the form 6*k-1.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The first prime is 2; 2^3 = 8, and 81331 = prime(7958), so a(1)=2.
The smallest prime p > 2 such that p^3//1331 yields a prime is p=107: 107^3 = 1225043, and 12250431331 = prime(552342812), so a(2)=107.

Mathematica

Select[Prime[Range[500]], PrimeQ[10000#^3+1331]&] (* Harvey P. Dale, May 30 2017 *)

Prog

(Magma) [p: p in PrimesUpTo(5000) | IsPrime(Seqint(Intseq(1331) cat Intseq(p^3)))]; // Vincenzo Librandi, Mar 05 2018

Crossrefs

Cf. A168327, A168417, A173836, A174213, A174260, A174229, A174355.

Sequence in context: A125593 A352496 A139887 * A340054 A267550 A224819

Adjacent sequences: A174406 A174407 A174408 * A174410 A174411 A174412

Keyword

base,nonn

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 19 2010

Status

approved