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%I #18 Dec 15 2017 17:35:49
%S 1,2,3,4,6,10,11,12,15,17,29,48,63,77,88,187,190,338,1133,1311,1832,
%T 2782,2907,3180,3272,5398,17530
%N Numbers n such that (prime(n)# + 4)/2 is a prime, where x# is the primorial A034386(x).
%C Numbers n such that [A002110(n)/2]+2 is prime.
%C These primes are products of consecutive odd primes plus 2: 2+[3.5.7.....p(n)] if n is here.
%C 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
%C a(28) > 25000. - _Robert Price_, Sep 29 2017
%t p = 1; Do[p = p*Prime[n]; If[PrimeQ[(p + 4)/2], Print[n]], {n, 1, 400} ]
%t Flatten[Position[FoldList[Times,Prime[Range[3000]]],_?(PrimeQ[ (#+4)/2]&)]] (* _Harvey P. Dale_, May 24 2015 *)
%o (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
%Y Cf. A002110, A067024, A065026.
%K nonn
%O 1,2
%A _Labos Elemer_, Dec 29 2001
%E More terms from _Robert G. Wilson v_, Dec 30 2001
%E a(19)-a(22) from _Jason Earls_, Dec 12 2006
%E a(23) from _Ray Chandler_, Jun 16 2013
%E a(24)-a(27) from _Robert Price_, Sep 29 2017
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