A093154 Primes resulting from serial multiplication of even composites, plus 1.

5, 193, 23041, 92897281, 980995276801, 23310331287699456001, 31888533201572855808001, 13532215908553332190020108288000001, 8829205774994708066835865418197893120000001, 945837910352576904120619801361499836578686566400000001

Offset: 1

Author

Enoch Haga, Mar 25 2004

Keywords

• easy
• nonn

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

Examples

			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.
		

Crossrefs

Cf. A093155, A248879.

Programs

Magma

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

Mathematica

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

Formula

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

Extensions

Edited and extended by Ray Chandler, Mar 27 2004

a(10) from Robert Price, Mar 10 2015