A063643 Primes with 2 representations: p*q - 2 = u*v + 2 where p, q, u and v are primes.

23, 37, 53, 67, 89, 113, 131, 157, 211, 251, 293, 307, 337, 379, 409, 449, 487, 491, 499, 503, 631, 683, 701, 719, 751, 769, 787, 919, 941, 953, 991, 1009, 1039, 1117, 1193, 1201, 1259, 1381, 1399, 1439, 1459, 1471, 1499, 1511, 1567, 1709, 1733, 1759, 1801

Offset: 1

Author

Reinhard Zumkeller, Jul 21 2001

Keywords

• nonn

Comments

Or, primes p such that p+/-2 are semiprimes. - Zak Seidov, Mar 08 2006

Examples

			A063643(25) = 751: 751 = A063637(60)= 753 - 2 = 3*251 - 2, 751 = A063638(55)= 749 + 2 = 7*107 + 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 term from T. D. Noe)

Crossrefs

Cf. A063637, A063638, A001358.

Cf. A109611 (Chen primes).

Programs

Maple

q:= p-> isprime(p) and map(numtheory[bigomega], {p-2, p+2})={2}:
select(q, [$2..2000])[];  # Alois P. Heinz, Apr 01 2024

Mathematica

Select[Prime[Range[300]], PrimeOmega[#+2] == PrimeOmega[#-2] == 2&] (* Jean-François Alcover, Mar 02 2019 *)

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

Formula

Intersection of A063637 and A063638. - Zak Seidov, Mar 14 2011