A112724 - OEIS

%I #6 Apr 17 2017 04:33:20

%S 2,6,600,210,866250,15732957240,156225655145328088320,7121261709511950

%N a(n) is the smallest number m such that the first n primes are all distinct prime divisors of m and for i=1,2,...,n prime(i)*m+1 is prime.

%C Next term is greater than 3*10^15.

%C a(9) > 10^30. - _Donovan Johnson_, Nov 15 2009

%C a(9) > 10^50. - _Giovanni Resta_, Apr 17 2017

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_334.htm">The Prime Puzzles & Problems connection</a>.

%e a(6)=15732957240 because {2,3,5,7,11,13}={prime(1),prime(2),..., prime(6)} is the set of all prime divisors of 15732957240;

%e all six numbers 2*15732957240+1,3*15732957240+1,5*15732957240+1, 7*15732957240+1,11*15732957240+1 & 13*15732957240+1 are prime and 15732957240 is the first number with such properties.

%Y Cf. A092023, A092024, A112723.

%K hard,nonn

%O 1,1

%A _Farideh Firoozbakht_, Nov 05 2005

%E a(7)-a(8) from _Donovan Johnson_, Nov 15 2009