A104877 Semiprimes of the form primorial(k) + 1.

30031, 9699691, 223092871, 13082761331670031, 117288381359406970983271, 7858321551080267055879091, 40729680599249024150621323471, 267064515689275851355624017992791

Offset: 1

Author

Jonathan Vos Post, Mar 28 2005

Keywords

• easy
• nonn

Examples

			6# + 1 = 2*3*5*7*11*13 + 1 = 30031 = 59 x 509.
8# + 1 = 2*3*5*7*11*13*17*19 + 1 = 9699691 = 347 x 27953.
9# + 1 = 2*3*5*7*11*13*17*19*23 + 1 = 223092871 = 317 x 703763.
14# + 1 = 2*3*5*7*11*13*17*19*23*29*31*37*41*43 + 1 = 13082761331670031 = 167 x 78339888213593.
		

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, A104876.

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 *)
Select[FoldList[Times,Prime[Range[30]]]+1,PrimeOmega[#]==2&] (* Harvey P. Dale, Oct 13 2022 *)

Formula

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