A168375 Natural numbers n for which the concatenation p= "1 n^3" (A168327) is prime.

1, 3, 13, 33, 39, 103, 109, 123, 139, 163, 169, 171, 181, 183, 207, 211, 289, 297, 303, 309, 339, 369, 379, 393, 423, 451, 457, 463, 1021, 1027, 1047, 1053, 1057, 1081, 1087, 1111, 1123, 1161, 1189, 1201, 1249, 1273, 1293, 1303, 1329, 1339, 1351, 1381, 1387

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 24 2009

Keywords

• nonn
• base

Comments

It is conjectured that sequence is infinite

Examples

			(1) "1 1^3"=10^1+1^3=11=prime(5) gives a(1)=1
(2) "1 3^3"=10^2+3^3=127=prime(31) gives a(2)=3
(3) "1 13^3"=10^4+13^3=12197=prime(1458) gives a(3)=13
		

References

• Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
• Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991
• Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996

Crossrefs

Cf. A000040 The prime numbers

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

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

Cf. A167535 Concatenation of two square numbers which give a prime

Formula

If n^3 is a d-digit natural number, odd and no multiple of 5, and d no multiple of 3, then p=10^d+n^3

Extensions

Edited by Charles R Greathouse IV, Apr 23 2010