A168417 Primes q for which 1 concatenated with q^3 (A168327) is prime.

3, 13, 103, 109, 139, 163, 181, 211, 379, 457, 463, 1021, 1087, 1123, 1201, 1249, 1303, 1381, 1579, 1597, 1609, 1699, 1861, 1873, 1987, 2011, 2029, 2053, 2143, 2221, 2281, 2341, 2473, 2503, 2557, 2731, 2857, 3061, 3067, 3217, 3253, 3271, 3319, 3331, 3517

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 25 2009

Keywords

• nonn
• base

Comments

It is conjectured that this sequence is infinite.

Examples

			(1) "1 3^3"=10^2+3^3=127=prime(31) gives a(1)=3=prime(2)
(2) "1 103^3"=10^7+103^3=11092727=prime(732258) gives a(3)=103=prime(27)
		

References

• Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
• Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005

Crossrefs

A168147 Primes of the form p = 1 + 10*n^3 for a natural number n

A168327 Primes of concatenated form p= "1 n^3"

A168375 Natural numbers n for which the concatenation p= "1 n^3" is prime

Programs

Mathematica

Select[Prime[Range[500]],PrimeQ[FromDigits[Join[{1},IntegerDigits[ #^3]]]]&] (* Harvey P. Dale, Jan 21 2013 *)

Extensions

Edited and extended by Charles R Greathouse IV, Apr 23 2010