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A087054
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Primes of the form pq + qr + rp where p, q and r are distinct primes.
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7
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31, 41, 59, 61, 71, 101, 103, 113, 131, 151, 167, 191, 199, 211, 227, 239, 241, 251, 263, 269, 271, 281, 293, 311, 331, 347, 359, 383, 401, 419, 421, 431, 439, 461, 467, 479, 487, 491, 503, 521, 541, 563, 571, 587, 599, 607, 617, 631, 641, 647, 653, 661, 691
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OFFSET
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1,1
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LINKS
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EXAMPLE
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A003415(2*3*19)=2*3+3*19+19*2=101=A000040(26), therefore 101 is a term (but also A003415(2*5*13)=2*5+5*13+13*2=101).
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MATHEMATICA
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sumProd[p_, q_, r_]:=p*q+p*r+q*r; pqrPrimes[nn_] := Module[{p=Prime[Range[PrimePi[(nn-6)/5]+1]], i, j, k, n}, Union[Reap[i=0; While[i++; sumProd[p[[i]], p[[i+1]], p[[i+2]]] <= nn, j=i; While[j++; sumProd[p[[i]], p[[j]], p[[j+1]]] <= nn, k=j; While[k++; n=sumProd[p[[i]], p[[j]], p[[k]]]; n <= nn, If[PrimeQ[n], Sow[n]]]]]][[2, 1]]]]; pqrPrimes[1000] (* T. D. Noe, Apr 27 2011 *)
nn=100; Take[Select[Union[Total[Times@@@Subsets[#, {2}]]&/@Subsets[ Prime[ Range[ nn]], {3}]], PrimeQ], nn] (* Harvey P. Dale, Jan 08 2013 *)
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PROG
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(PARI) list(lim)=my(v=List()); forprime(r=5, (lim-6)\5, forprime(q=3, min((lim-2*r)\(r+2), r-2), my(S=q+r, P=q*r); forprime(p=2, min((lim-P)\S, q-1), isprime(p*S+P) && listput(v, p*S+P)))); Set(v) \\ Charles R Greathouse IV, Feb 26 2014
(PARI) is(n)=forprime(r=(sqrtint(3*n-3)+5)\3, (n-6)\5, forprime(q= sqrtint(r^2+n)-r+1, min((n-2*r)\(r+2), r-2), if((n-q*r)%(q+r)==0 && isprime((n-q*r)/(q+r)), return(isprime(n))))); 0 \\ Charles R Greathouse IV, Feb 26 2014
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CROSSREFS
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Cf. A087053 (numbers of the form pq+qr+rp).
Cf. A189759 (p*q*r for primes of this form).
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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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