

A201613


Primes of the form p^2 + 2q^2 with p and q odd primes.


3



43, 59, 67, 107, 139, 251, 307, 347, 379, 547, 587, 859, 1699, 1867, 1931, 3371, 3499, 3739, 4507, 5059, 5347, 6907, 6971, 7451, 10091, 10627, 10667, 11467, 12491, 18787, 20411, 21227, 22907, 29947, 32059, 32779, 37547, 38651, 39619, 49307, 49747, 53147, 55787
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OFFSET

1,1


COMMENTS

One of primes p, q must be 3, hence we have two sets of primes: 9+2*p^2 and p^2+18 with p > 3.
Note that if we allow 2 for p or q then there is another "set" of primes of the form p^2+8 (q=2) with odd prime p  this set contains only the prime 17=3^2+8.


LINKS



EXAMPLE

43=5^2+2*3^2, 59=3^2+2*5^2, 67=7^2+2*3^2.


PROG

(PARI) list(lim)=my(v=List(), t); forprime(p=5, sqrtint(lim\118), if(isprime(t=p^2+18), listput(v, t))); forprime(q=5, sqrtint((lim9)\2), if(isprime(t=2*q^2+9), listput(v, t))); Set(v) \\ Charles R Greathouse IV, Aug 26 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



