A177014 a(n) is the smallest number m such that all the n numbers 1!*m+1, 2!*m+1, ..., n!*m+1 are prime.

1, 1, 1, 18, 18, 8628, 748668, 2506980, 228698250, 228698250

Offset: 1

Author

Enoch Haga and Farideh Firoozbakht, May 20 2010

Keywords

• more
• nonn

Examples

			a(5)=18 because each of the five numbers 1!*18+1, 2!*18+1, 3!*18+1, 4!*18+1 and 5!*18+1 is prime, and 18 is the smallest such number.
The corresponding primes are:
n=1:  2;
n=2:  2, 3;
n=3:  2, 3, 7;
n=4:  19, 37, 109, 433;
n=5:  19, 37, 109, 433, 2161;
n=6:  8629, 17257, 51769, 207073, 1035361, 6212161;
n=7:  748669, 1497337, 4492009, 17968033, 89840161, 539040961, 3773286721;
  ...
		

Crossrefs

Cf. A177013.

Programs

PARI

okm(m, n) = {for (k=1, n, if (! isprime(k!*m+1), return (0));); return (1);}
a(n) = {m = 1; while(! okm(m, n), m++); m;} \\ Michel Marcus, Jun 08 2014

Extensions

a(10) corrected by Jon E. Schoenfield, Mar 07 2018