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