A168540 Natural numbers n for which 100n^3 + 27 is prime.

1, 2, 4, 5, 7, 13, 17, 25, 29, 32, 44, 55, 61, 76, 77, 80, 92, 106, 109, 112, 116, 121, 124, 136, 137, 142, 143, 149, 152, 154, 158, 161, 169, 170, 178, 190, 191, 196, 200, 208, 221, 223, 224, 227, 230, 245, 254, 259, 260, 262

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 29 2009

Keywords

• nonn

Comments

It is conjectured that sequence is infinite.

Examples

			(1) 3^3+10^2*1^3=127=prime(31) gives a(1)=1
(2) 3^3+10^2*2^3=827=prime(144) gives a(2)=2
(3) 3^3+10^2*13^3=219727=prime(19588) gives a(6)=13
		

References

• Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
• Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991

Crossrefs

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

Programs

Mathematica

Select[Range[300],PrimeQ[100#^3+27]&] (* Harvey P. Dale, May 10 2013 *)

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010