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%I #30 Oct 30 2023 11:00:40
%S 11,17,23,37,41,53,59,67,71,79,89,97,113,131,157,163,179,211,223,239,
%T 251,269,293,307,311,331,337,367,373,379,383,397,409,419,439,449,487,
%U 491,499,503,521,547,593,599,613,631,673,683,691,701,709,719,733,739
%N Primes p such that p-2 is a semiprime.
%C Primes of form p*q + 2, where p and q are primes.
%C 11 is the only prime of this form where p=q. For prime p>3, 3 divides p^2+2. - _T. D. Noe_, Mar 01 2006
%C The asymptotic growth of this sequence is relevant for A204142. We have a(10^k) = (11, 79, 1571, 27961, 407741, 5647823, ...). - _M. F. Hasler_, Feb 13 2012
%H M. F. Hasler, <a href="/A063638/b063638.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A241809(n) + 2. - _Hugo Pfoertner_, Oct 30 2023
%t Take[Select[ # + 2 & /@ Union[Flatten[Outer[Times, Prime[Range[100]], Prime[Range[100]]]]], PrimeQ], 60]
%t Select[Prime[Range[200]],PrimeOmega[#-2]==2&] (* _Paolo Xausa_, Oct 30 2023 *)
%o (PARI) n=0; for (m=2, 10^9, p=prime(m); if (bigomega(p - 2) == 2, write("b063638.txt", n++, " ", p); if (n==1000, break))) \\ _Harry J. Smith_, Aug 26 2009
%o (PARI) forprime(p=3,9999, bigomega(p-2)==2 & print1(p","))
%o (PARI) p=2; for(n=1,1e4, until(bigomega(-2+p=nextprime(p+1))==2,); write("b063638.txt", n" "p)) \\ _M. F. Hasler_, Feb 13 2012
%o (PARI) list(lim)=my(v=List(), t); forprime(p=3, (lim-2)\3, forprime(q=3, min((lim-2)\p, p), t=p*q+2; if(isprime(t), listput(v, t)))); Set(v) \\ _Charles R Greathouse IV_, Aug 05 2016
%o (Haskell)
%o a063638 n = a063638_list !! (n-1)
%o a063638_list = map (+ 2) $ filter ((== 1) . a064911) a040976_list
%o -- _Reinhard Zumkeller_, Feb 22 2012
%Y Cf. A005385, A001358, A063637, A109611 (Chen primes), A204142, A064911, A040976, A241809.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jul 21 2001
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