A071621 Primes that can be written as "a * b + c * d", where a, b, c and d are also primes.

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

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]
Take[Select[Union[Total[Times@@@TakeDrop[#, 2]]&/@Tuples[Prime[Range[15]], 4]], PrimeQ], 60] (* Harvey P. Dale, Dec 04 2024 *)

Prog

(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
(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