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%I #29 Apr 01 2024 13:27:40
%S 23,37,53,67,89,113,131,157,211,251,293,307,337,379,409,449,487,491,
%T 499,503,631,683,701,719,751,769,787,919,941,953,991,1009,1039,1117,
%U 1193,1201,1259,1381,1399,1439,1459,1471,1499,1511,1567,1709,1733,1759,1801
%N Primes with 2 representations: p*q - 2 = u*v + 2 where p, q, u and v are primes.
%C Or, primes p such that p+/-2 are semiprimes. - _Zak Seidov_, Mar 08 2006
%H Alois P. Heinz, <a href="/A063643/b063643.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 term from T. D. Noe)
%F Intersection of A063637 and A063638. - _Zak Seidov_, Mar 14 2011
%e A063643(25) = 751: 751 = A063637(60)= 753 - 2 = 3*251 - 2, 751 = A063638(55)= 749 + 2 = 7*107 + 2.
%p q:= p-> isprime(p) and map(numtheory[bigomega], {p-2, p+2})={2}:
%p select(q, [$2..2000])[]; # _Alois P. Heinz_, Apr 01 2024
%t Select[Prime[Range[300]], PrimeOmega[#+2] == PrimeOmega[#-2] == 2&] (* _Jean-François Alcover_, Mar 02 2019 *)
%o (PARI) { n=0; for (m=2, 10^9, p=prime(m); if (bigomega(p + 2) == 2 && bigomega(p - 2) == 2, write("b063643.txt", n++, " ", p); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 26 2009
%Y Cf. A063637, A063638, A001358.
%Y Cf. A109611 (Chen primes).
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Jul 21 2001
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