A093155 Primes resulting from serial multiplication of even composites, minus 1.

3, 23, 191, 23039, 322559, 5160959, 40874803199, 25505877196799

Offset: 1

Author

Enoch Haga, Mar 25 2004

Keywords

• easy
• nonn

Comments

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

a(9) has 193 digits, a(10) has 230 digits. - Vincenzo Librandi, Mar 08 2015

Examples

			a(1) = 3 = 2*2! - 1.
a(2) = 23 = 2^2*3! - 1.
a(3) = 191 = 2^3*4! - 1.
a(4) = 23039 = 2^5*6! - 1.
a(5) = 322559 = 2^6*7! - 1.
a(6) = 5160959 = 2^7*8! - 1.
a(7) = 40874803199 = 2^10*11! - 1.
a(8) = 25505877196799 = 2^12*13! - 1.
a(9) = 2^101*102! - 1 is too large to include.
a(10) = 2^117*118! - 1; a(11) = 2^227*228! - 1. - _Jorge Coveiro_, Dec 24 2004
		

Crossrefs

Cf. A093154, A101323.

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is 2^n*Factorial(n+1)-1]; // Vincenzo Librandi, Mar 08 2015

Mathematica

Select[Table[2^n (n + 1)! - 1, {n, 0, 300}], PrimeQ] (* Vincenzo Librandi, Mar 08 2015 *)

PARI

for(x=1,500,if(isprime(2^x*(x+1)!-1),print1(x, ", "))) \\ Jorge Coveiro, Dec 24 2004

Formula

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

Extensions

Edited by Ray Chandler, Mar 27 2004

The next term is too large to include.