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A067027
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Numbers n such that (prime(n)# + 4)/2 is a prime, where x# is the primorial A034386(x).
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25
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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