A176781 Smallest prime prime(i) such that concatenation 2//0_(n)//prime(i) is prime.

3, 11, 3, 17, 3, 3, 3, 11, 89, 41, 257, 3, 29, 131, 353, 3, 3, 11, 89, 521, 257, 3, 17, 3, 467, 89, 149, 17, 71, 47, 293, 17, 191, 47, 3, 41, 23, 11, 401, 41, 443, 41, 293, 479, 311, 23, 587, 41, 1289, 1013, 29, 41, 59, 293, 1031, 17, 23, 17, 347, 401, 599, 11, 227, 827, 401

Offset: 0

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 26 2010

Keywords

• base
• nonn

Comments

We search for the prime such that the first prime (=2) concatenated with n zeros and concatenated with that prime is again a prime number.

If p = prime(i) is a d(i)-digit prime: q = 2 * 10^(n+d(i)) + p has to be prime.

Necessarily prime(i) is congruent to 2 (mod 3).

It is conjectured that prime(i) = 3 occurs infinitely often: at n= 0, 2, 4, 5, 6, 11, 15, 16, 21, 23, 34, 114, 119,...

Examples

			n = 0: 2//3 = 23 = prime(9), 3 = prime(2) is first term
n = 1: 2//0//11 = 2011 = prime(305), 11 = prime(5) is 2nd term
n = 2: 2//00//3 = 2003 = prime(304), 3 = prime(2) is 3rd term
		

References

• E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig/Jena/ Berlin 1982

Crossrefs

Cf. A164968, A173291, A176316

Extensions

Offset corrected and sequence extended by R. J. Mathar, Apr 28 2010