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

Author

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

Keywords

• base
• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Magma

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

Mathematica

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