OFFSET

1,1

COMMENTS

Primes of the form 2^n*(n+1)!+1.

a(12) = 2^118*119!+1, a(13) = 2^142*143!+1. I conjecture that a(13) is the last prime number of this form. - Jorge Coveiro, Apr 01 2004

Conjecture that a(13) is the last prime of this form is false:

a(14) = 2^2789*2780!+1 is prime

a(15) = 2^3142*3143!+1 is prime

a(16) = 2^3557*3558!+1 is prime

a(17) = 2^3686*3687!+1 is prime

a(18) = 2^4190*4191!+1 is prime

a(19) = 2^7328*7329!+1 is prime

See A248879. - Robert Price, Mar 10 2015

FORMULA

Starting with 4, multiply even composites until the product plus 1 equals a prime.

EXAMPLE

a(1) = 5 = 2*2!+1

a(2) = 193 = 2^3*4!+1

a(3) = 23041 = 2^5*6!+1

a(4) = 92897281 = 2^8*9!+1

a(5) = 980995276801 = 2^11*12!+1

a(6) = 23310331287699456001 = 2^16*17!+1

a(11) = 2^87*88!+1 is too large to include.

MATHEMATICA

Select[Table[2^n (n + 1)! + 1, {n, 1, 100}], PrimeQ] (* Vincenzo Librandi, Mar 10 2015 *)

PROG

(Magma) [a: n in [1..40] | IsPrime(a) where a is 2^n*Factorial(n+1)+1]; // Vincenzo Librandi, Mar 10 2015

CROSSREFS

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Mar 25 2004

EXTENSIONS

Edited and extended by Ray Chandler, Mar 27 2004

a(10) from Robert Price, Mar 10 2015

STATUS

approved