OFFSET
1,1
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.
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 28 2005
STATUS
approved