A173291 Smallest prime p such that the concatenation of p and prime(n) is a prime, or 0 if no other number exists.

0, 2, 0, 3, 2, 3, 3, 7, 2, 2, 3, 3, 2, 7, 3, 3, 3, 7, 3, 2, 3, 3, 2, 3, 3, 5, 7, 5, 3, 2, 7, 2, 2, 19, 11, 7, 19, 3, 3, 9, 2, 3, 3, 7, 5, 37, 7, 31, 5, 3, 5, 2, 13, 2, 3, 41, 2, 3, 31, 2, 7, 2, 3, 2, 3, 11, 3, 13, 2, 7, 11, 3, 13, 3, 19, 2, 2, 13, 17, 37, 5, 13, 5, 3, 139, 5, 3, 3, 3, 3, 2, 5, 7, 3, 3

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 15 2010

Keywords

• base
• nonn

Comments

If prime(n) has k digits then a(k) is the smallest prime(m) where 10^k * prime(m) + prime(n) is a prime.

In base 10, no prime can be prefixed to 2 or 5 to make another prime.

Examples

			a(2) = 2 because prime(2) = 3, and the concatenation of 2 and 3 gives the prime 23.
a(3) = 0 because prime(3) = 5 and there is no prime to concatenate with to give another prime.
a(4) = 3 because prime(5) = 7 but the concatenation with 2 gives 27 = 3^3, so it has to be 3 in order to give 37, which is prime.
		

References

• John Derbyshire, Prime obsession. Joseph Henry Press, Washington, DC 2003
• Marcus du Sautoy, Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004
• Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005

Crossrefs

Cf. A088606, A167764, A168327, A168417, A030469.