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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
2, 6, 600, 210, 866250, 15732957240, 156225655145328088320, 7121261709511950 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 28 17:45 EDT 2022. Contains 357080 sequences. (Running on oeis4.)