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%I #12 Oct 13 2022 11:34:07
%S 30031,9699691,223092871,13082761331670031,117288381359406970983271,
%T 7858321551080267055879091,40729680599249024150621323471,
%U 267064515689275851355624017992791
%N Semiprimes of the form primorial(k) + 1.
%H Sebastian Martin Ruiz, <a href="https://www.jstor.org/stable/3619207">A Result on Prime Numbers</a>, Math. Gaz. 81, 269, 1997.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>
%F n# + 1 iff semiprime. Equals {A002110(i) + 1} intersection {A001358(j)}.
%e 6# + 1 = 2*3*5*7*11*13 + 1 = 30031 = 59 x 509.
%e 8# + 1 = 2*3*5*7*11*13*17*19 + 1 = 9699691 = 347 x 27953.
%e 9# + 1 = 2*3*5*7*11*13*17*19*23 + 1 = 223092871 = 317 x 703763.
%e 14# + 1 = 2*3*5*7*11*13*17*19*23*29*31*37*41*43 + 1 = 13082761331670031 = 167 x 78339888213593.
%t 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 *)
%t Select[FoldList[Times,Prime[Range[30]]]+1,PrimeOmega[#]==2&] (* _Harvey P. Dale_, Oct 13 2022 *)
%Y Cf. A001358, A002110, A034386, A005234, A014545, A018239, A006794, A057704, A057705, A104876.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 28 2005
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