A090188 Primes P such that P=k*p(n)#-p(n+1) is prime for least k. Here p(i)# denotes the i-th primorial and p(i) denotes the i-th prime.

3, 7, 23, 199, 2297, 30013, 1021001, 9699667, 669278581, 32348466119, 401120980223, 29682952539199, 1825501581163217, 39248283995010043, 3074448912942456997, 228124109340330313051, 49991769104009528615759

Offset: 1

Author

Pierre CAMI, Jan 21 2004

Keywords

• base
• nonn

Comments

k*p(n)#-p(n+1) is the greatest prime < k*p(n)#-p(n+1)-1 and if k*p(n)#-p(n+1)-1 is not prime it is the greatest prime < k*p(n)#-p(n+1). Values for k are given in A090189.

Examples

			1*2*3*5*7*11*13-17=30013, 1*p(6)#-p(7)=30013, 1 is the least k for n=6
30013 is prime P for n=6.
		

Programs

PARI

a(n)=my(P=prod(i=1,n,prime(i)),q=prime(n+1),k);while(!ispseudoprime(P*k++ - q), ); k*P-q \\ Charles R Greathouse IV, Feb 07 2013

Extensions

a(14) corrected by Charles R Greathouse IV, Feb 07 2013