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%I #6 Nov 05 2015 10:46:27
%S 13,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,
%T 109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,
%U 199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293
%N Primes that can be written as "a * b + c * d", where a, b, c and d are also primes.
%C As size in the Mathematica coding is increased, the primes not previously covered will probably be forthcoming. Conjecture: Only the primes 2, 3, 5, 7, 11 and 17 are not representable by this form.
%H Charles R Greathouse IV, <a href="/A071621/b071621.txt">Table of n, a(n) for n = 1..10000</a>
%e 13 = 2*2 + 3*3, so 13 belongs to the sequence.
%t size = 15; Select[ Union[ Flatten[ Table[ ppp = Prime[i]Prime[j] + Prime[k]Prime[l]; If[ PrimeQ[ppp], Print[{Prime[i], Prime[j], Prime[k], Prime[l], ppp}]]; ppp, {i, size}, {j, size}, {k, size}, {l, size} ]]], PrimeQ]
%o (PARI) list(lim)=my(v=vectorsmall(lim\1),u=List(),t); forprime(p=3,lim\2-2, forprime(q=2,min(p,(lim-4)\p), t=p*q; forprime(r=2,(lim-t)\2, v[t+2*r]=1))); forprime(i=1,lim,if(v[i],listput(u,i))); v=0; Set(u) \\ _Charles R Greathouse IV_, Nov 05 2015
%o (PARI) a(n)=if(n>1,prime(n+6),13) \\ _Charles R Greathouse IV_, Nov 05 2015
%K nonn
%O 1,1
%A Arnoud Buzing (arnoudb(AT)wolfram.com), Jun 21 2002
%E Edited by _Robert G. Wilson v_, Jun 25 2002
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