A104876 Semiprimes of the form primorial(k) - 1.

209, 510509, 6469693229, 200560490129, 13082761331670029, 1922760350154212639069, 557940830126698960967415389, 40729680599249024150621323469, 2305567963945518424753102147331756069, 232862364358497360900063316880507363069

Offset: 1

Author

Jonathan Vos Post, Mar 28 2005

Keywords

• easy
• nonn

Examples

			4# - 1 = 209 = 11 * 19.
7# - 1 = 510509 = 61 * 8369.
10# - 1 = 6469693229 = 79 * 81894851.
		

Links

• Sebastian Martin Ruiz, A Result on Prime Numbers, Math. Gaz. 81, 269, 1997.
• Eric Weisstein's World of Mathematics, Primorial.
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Cf. A001358, A002110, A034386, A005234, A014545, A018239, A006794, A057704, A057705, A104877.

Programs

Mathematica

Bigomega[n_]:=Plus@@Last/@FactorInteger[n]; SemiprimeQ[n_]:=Bigomega[n]==2; Primorial[n_]:=Product[Prime[i], {i, n}]; Select[Table[Primorial[n]-1, {n, 30}], SemiprimeQ] (* Ray Chandler, Mar 28 2005 *)

Formula

n# - 1 iff semiprime. Equals {A002110(i) - 1} intersection {A001358(j)}.

Extensions

Entry revised by N. J. A. Sloane, Apr 01 2006