A173733 Primes p which give primes when 1331 = 11^3 is prefixed (see A173579).

3, 17, 53, 83, 107, 227, 251, 269, 293, 347, 383, 431, 443, 521, 587, 599, 641, 647, 683, 719, 761, 773, 821, 857, 929, 1031, 1097, 1217, 1223, 1301, 1367, 1409, 1433, 1451, 1619, 1637, 1709, 1787, 1973, 2081, 2087, 2129, 2399, 2477, 2591, 2633, 2657, 2693

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 23 2010

Keywords

• nonn
• base
• less

Comments

N = 1331 = 11^3, p k-digit prime, to check if q = N * 10^k + p is prime

With exception of 3 necessarily p of form 3k+2, as sod(1331 = 8)

Examples

			13313 = prime(1581) => a(1) = prime(2) = 3
133117 = prime(12425) => a(2) = prime(7) = 17
133153 = prime(12427) => a(3) = prime(16) = 53
13311217 = prime(868166) => a(28) = prime(199) = 1217
13311223 = prime(868167) => a(29) = prime(200) = 1223
Note: two consecutive primes P = prime(n), Q = prime(n+1) yield consecutive prime concatenations "N P" = prime(m) and "N Q" = prime(m+1)
		

References

• K. Haase, P. Mauksch: Spass mit Mathe, Urania-Verlag Leipzig, Verlag Dausien Hanau, 2. Auflage 1985
• Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A102006, A167535, A168147, A168219, A168274, A173579

Programs

Mathematica

Select[Prime[Range[400]],PrimeQ[FromDigits[Join[{1,3,3,1}, IntegerDigits[ #]]]]&] (* Harvey P. Dale, Jun 09 2015 *)

Extensions

Edited and extended by Charles R Greathouse IV, Apr 24 2010