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

1,2

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.

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

Links

Table of n, a(n) for n=1..95.

Example

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.

Crossrefs

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

Sequence in context: A277890 A243403 A051613 * A341889 A078031 A077961

Adjacent sequences: A173288 A173289 A173290 * A173292 A173293 A173294

Keyword

base,nonn

Author

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

Status

approved