A084406 Numbers k such that k#*2^k-1 is prime, where k# = product of primes <= k.

2, 3, 7, 8, 14, 16, 18, 20, 40, 42, 44, 53, 134, 154, 185, 187, 191, 197, 200, 201, 230, 235, 239, 244, 256, 282, 303, 358, 489, 536, 665, 684, 719, 1098, 1204, 1400, 1516, 1629, 1903, 1997, 1999, 2104, 2477, 3075, 3676, 3785, 4115, 5429, 5808, 6069, 6276, 9095

Offset: 1

Author

Jason Earls, Jun 24 2003

Keywords

• nonn

Comments

The values corresponding to terms 1098 through 1516 have been proved to be prime.

No more terms < 10000. - L. Joris Perrenet, Mar 18 2020

Links

• The OpenPFGW Project, Primality Tester.

Crossrefs

Cf. A034386.

Programs

Mathematica

p = 1; Do[If[PrimeQ[n], p *= n]; If[PrimeQ[p*2^n - 1], Print[n]], {n, 2, 10000}] (* Ryan Propper, Sep 05 2005 *)
Select[Table[{k,Times@@Prime[Range[PrimePi[k]]]},{k,720}],PrimeQ[#[[2]]2^#[[1]]-1]&][[;;,1]] (* The program generates the first 33 terms of the sequence. *) (* Harvey P. Dale, Jan 20 2024 *)

Extensions

More terms from Ryan Propper, Sep 05 2005

a(52) from L. Joris Perrenet, Mar 18 2020