A169586 Primes p in A168540 for which q = 3^3 + 10^2*p^3 (A168487) is prime.

2, 5, 7, 13, 17, 29, 61, 109, 137, 149, 191, 223, 227, 269, 311, 331, 337, 359, 389, 397, 409, 433, 457, 467, 491, 587, 619, 653, 661, 709, 727

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 02 2009

Keywords

• nonn

Comments

It is conjectured that sequence is infinite

Examples

			(1) 3^3+10^2*2^3=827=prime(144) gives a(1)=2=prime(1)
(2) 3^3+10^2*5^3=12527=prime(1496) gives a(2)=5=prime(3)
(3) 3^3+10^2*13^3=219727=prime(19588) gives a(4)=13=prime(6)
		

References

• Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
• Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005
• Arnold Scholz, Bruno Schoeneberg: Einführung in die Zahlentheorie, Walter de Gruyter, 5. Auflage 1973

Crossrefs

A000040 The prime numbers

A167535 Concatenation of two square numbers which give a prime

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 Naturals n for which the concatenation p= "1 n^3"is prime

A168487 Primes of form p = 3^3 + 10^2*n^3 with a natural number n

A168540 Naturals n for which the concatenation p = 3^3 + 10^2*n^3 is prime