A108519 a(n) is the smallest natural number m such that (10^n)! - m is prime.

11, 271, 6701, 40471

Offset

1,1

Comments

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

(10^4)!-40471 is a probable prime. - Jason Yuen, May 20 2024

Links

Table of n, a(n) for n=1..4.

Formula

a(n) = A033933(10^n). - Jason Yuen, May 20 2024

Example

a(3)=6701 because (10^3)!-6701 is prime and for 0<m<6701 1000!-m is
composite.

Mathematica

a[n_] := (For[m = 1, ! PrimeQ[(10^n)! - m], m++ ]; m); Do[Print[a[n]], {n, 3}]

Crossrefs

Cf. A108518, A033933.

Sequence in context: A285051 A267900 A168147 * A160195 A203240 A062210

Adjacent sequences: A108516 A108517 A108518 * A108520 A108521 A108522

Keyword

more,nonn,hard

Author

Farideh Firoozbakht, Jul 10 2005

Extensions

a(4) from Jason Yuen, May 20 2024

Status

approved