A115785 Smallest prime number p such that p - prime(1)#, p - prime(2)#, ..., p - prime(n)# are all prime, where prime(i)# is the primorial of the i-th prime (A002110(i)).

5, 13, 43, 229, 3463, 43789, 1088449, 19800379, 264333259, 9348884059, 228178314439, 7931712374479, 307867708410673, 13230211614496609, 618681508598750923

Offset: 1

Author

Rick L. Shepherd, Jan 31 2006

Keywords

• nonn
• more

Comments

Subset of A006512 (greater of twin primes).

Inspired by C. Rivera's Prime Curio for 313. a(4) = 229 is the smallest prime having the same property he states for 313.

Examples

			a(4) = 229 because 229, 229 - 2, 229 - 2*3, 229 - 2*3*5 and 229 - 2*3*5*7 are all prime and there is no smaller prime with this property.
		

Links

• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 313
• Carlos Rivera, Puzzle 350. Primes & primorials, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A002110, A006512, A115786 (for p + prime(i)#).

Extensions

a(10) from Don Reble, Feb 15 2006

More terms from Jens Kruse Andersen, Feb 26 2006