A108518 a(n) is the smallest natural number m such that (10^n)! + m is prime.

1, 11, 229, 1283, 44159

Offset: 0

Author

Farideh Firoozbakht, Jul 10 2005

Keywords

• more
• nonn
• hard

Comments

If a(n) is composite then a(n)>10^(2n)+2*10^n. Conjecture: All terms are noncomposite numbers.

(10^4)!+44159 is a probable prime. - Jason Yuen, May 20 2024

Examples

			a(3)=1283 because (10^3)!+1283 is prime and for 0<m<1283 1000!+m is
composite.
		

Crossrefs

Cf. A108519, A033932.

Programs

Mathematica

a[n_] := (For[m = 1, ! PrimeQ[(10^n)! + m], m++ ]; m); Do[Print[a[n]], {n, 0, 3}]
sp[n_]:=Module[{c=(10^n)!},NextPrime[c]-c]; Array[sp,4,0] (* Harvey P. Dale, Jul 29 2013 *)

Formula

a(n) = A033932(10^n). - Jason Yuen, May 20 2024

Extensions

a(4) from Jason Yuen, May 20 2024