

A071621


Primes that can be written as "a * b + c * d", where a, b, c and d are also primes.


3



13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293
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OFFSET

1,1


COMMENTS

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.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

13 = 2*2 + 3*3, so 13 belongs to the sequence.


MATHEMATICA

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]


PROG

(PARI) list(lim)=my(v=vectorsmall(lim\1), u=List(), t); forprime(p=3, lim\22, forprime(q=2, min(p, (lim4)\p), t=p*q; forprime(r=2, (limt)\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
(PARI) a(n)=if(n>1, prime(n+6), 13) \\ Charles R Greathouse IV, Nov 05 2015


CROSSREFS

Sequence in context: A274407 A054986 A210582 * A240565 A160951 A038888
Adjacent sequences: A071618 A071619 A071620 * A071622 A071623 A071624


KEYWORD

nonn


AUTHOR

Arnoud Buzing (arnoudb(AT)wolfram.com), Jun 21 2002


EXTENSIONS

Edited by Robert G. Wilson v, Jun 25 2002


STATUS

approved



