

A112724


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.


3




OFFSET

1,1


COMMENTS

Next term is greater than 3*10^15.
a(9) > 10^30.  Donovan Johnson, Nov 15 2009
a(9) > 10^50.  Giovanni Resta, Apr 17 2017


LINKS

Table of n, a(n) for n=1..8.
Carlos Rivera, The Prime Puzzles & Problems connection.


EXAMPLE

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;
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.


CROSSREFS

Cf. A092023, A092024, A112723.
Sequence in context: A114628 A135424 A132495 * A110795 A179860 A067107
Adjacent sequences: A112721 A112722 A112723 * A112725 A112726 A112727


KEYWORD

hard,nonn


AUTHOR

Farideh Firoozbakht, Nov 05 2005


EXTENSIONS

a(7)a(8) from Donovan Johnson, Nov 15 2009


STATUS

approved



