A180950 Smallest prime such that the sum of successive 11 primes is a prime.

5, 7, 11, 13, 19, 23, 37, 41, 59, 101, 103, 107, 109, 113, 137, 149, 151, 157, 167, 173, 191, 269, 281, 283, 293, 307, 331, 349, 353, 359, 421, 431, 463, 479, 487, 499, 503, 569, 599, 607, 613, 617, 619, 677, 733, 761, 773, 823, 853, 883, 967, 977, 1051, 1087

Offset: 1

Author

Carmine Suriano, Sep 27 2010

Keywords

• nonn

Comments

Sum i=0 to 10 of prime(n+i) is a prime.

There are many twins: (11,13); (149,151); (1301,1303); (1997,1999); (8969,8971) ...

There are also consecutive primes: (101,103,107,109,113); (607,613,617,619); (8681,8689,8693)

Examples

			a(5)=19 since 19+23+29+31+37+41+43+47+53+59+61=443 is a prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A127338, A073681, A152468, A180948, A189571, A226380.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[500]], 11, 1], PrimeQ[Total[#]] &]][[1]] [[1]] (* Harvey P. Dale, Jun 05 2013 *)
Prime[Select[Range[200], PrimeQ[Sum[Prime[# + i], {i, 0, 10}]] &]] (* Bruno Berselli, Aug 22 2013 *)

Extensions

More cross references from Harvey P. Dale, Jun 05 2013