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 A067027 Numbers n such that (prime(n)# + 4)/2 is a prime, where x# is the primorial A034386(x). 25
 1, 2, 3, 4, 6, 10, 11, 12, 15, 17, 29, 48, 63, 77, 88, 187, 190, 338, 1133, 1311, 1832, 2782, 2907, 3180, 3272, 5398, 17530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers n such that [A002110(n)/2]+2 is prime. These primes are products of consecutive odd primes plus 2: 2+[3.5.7.....p(n)] if n is here. a(19)-a(22) are Fermat and Lucas PRPs. (prime(2782)# + 4)/2 has 10865 digits. PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (p(2782)#+4)/2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) (p(2782)#+4)/2 is Fermat and Lucas PRP! - Jason Earls, Dec 12 2006 a(28) > 25000. - Robert Price, Sep 29 2017 LINKS MATHEMATICA p = 1; Do[p = p*Prime[n]; If[PrimeQ[(p + 4)/2], Print[n]], {n, 1, 400} ] Flatten[Position[FoldList[Times, Prime[Range[3000]]], _?(PrimeQ[ (#+4)/2]&)]] (* Harvey P. Dale, May 24 2015 *) PROG (PARI) n=0; pr=1/2; forprime(p=2, 1e4, n++; pr*=p; if(ispseudoprime(pr+2), print1(n", "))) \\ Charles R Greathouse IV, Jul 25 2011 CROSSREFS Cf. A002110, A067024, A065026. Sequence in context: A339670 A047417 A066936 * A275108 A005457 A005453 Adjacent sequences:  A067024 A067025 A067026 * A067028 A067029 A067030 KEYWORD nonn AUTHOR Labos Elemer, Dec 29 2001 EXTENSIONS More terms from Robert G. Wilson v, Dec 30 2001 a(19)-a(22) from Jason Earls, Dec 12 2006 a(23) from Ray Chandler, Jun 16 2013 a(24)-a(27) from Robert Price, Sep 29 2017 STATUS approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)