A174858 Primes p of a prime triple (p,p+2,p+6) such that the concatenation p//(p+2)//(p+6) is prime.

5, 11, 17, 41, 11171, 16061, 16187, 20897, 29021, 34841, 36011, 39227, 41177, 51341, 55331, 56891, 58907, 63311, 64151, 69191, 77261, 82757, 113021, 122027, 123731, 135461, 151337, 167621, 173291, 174761, 187631, 191447, 195731, 203207, 203381, 225341, 227531

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Mar 31 2010

Keywords

• base
• nonn
• uned

Comments

If p is a d-digit prime of a triple: p*10^(2*d) + (p+2)*10^d + p+6 = (10^(2*d)+10^d+1) * p + 2*(10^d+3) to be a prime.

No such concatenation exists for a 4-digit p: d=4, p*10^8 + (p+2)*10^4 + p+6 = p*(10^8 + 10^4 + 1) + 2*10^4 + 6, coefficients (10^8 + 10^4 + 1) and 2*(10^4 + 3) have both divisor 7.

Examples

			(5,7,11) is 1st prime triple, 5711 = prime(752), 5 is 1st term of sequence
(11,13,17) is 2nd prime triple, 111317 = prime(10561), 11 is 2nd term of sequence
		

Links

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

Crossrefs

Cf. A022004.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[20000]],3,1],Differences[#]=={2,4} && PrimeQ[ FromDigits[Flatten[IntegerDigits/@#]]]&]][[1]] (* Harvey P. Dale, Apr 10 2013 *)