A176316 Primes p with property that concatenation prime(1)//p//prime(2) = 2//p//3 is a prime.

2, 3, 11, 29, 47, 59, 71, 83, 101, 131, 149, 167, 227, 257, 317, 347, 359, 383, 389, 479, 503, 563, 569, 587, 593, 683, 773, 839, 857, 881, 947, 983, 1019, 1091, 1109, 1187, 1193, 1229, 1259, 1319, 1361, 1499, 1583, 1613, 1637, 1697, 1733, 1823, 1913, 1931

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

Necessarily for p > 3: p = 6 * m + 5, as for q = 6*m+1 sod(2//q//3) is a multiple of 3

Examples

			223 = prime(48), 2 = prime(1) is first term
233 = prime(51), 3 = prime(2) is 2nd term
2//05//3 = 2053 = prime(310), a "leading" zero is included, no term of sequence
2113 = prime(319), 11 = prime(5) is 3rd term
		

References

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

filter:= p -> isprime(p) and isprime(10*p+3+2*10^(2+ilog10(p))):
select(filter, [2,3,seq(i,i=5..2000,6)]); # Robert Israel, Nov 29 2017