|
|
A139862
|
|
Primes of the form 5x^2 + 26y^2.
|
|
1
|
|
|
5, 31, 71, 109, 149, 151, 229, 239, 271, 349, 359, 421, 431, 461, 479, 509, 541, 631, 661, 709, 821, 839, 941, 1021, 1061, 1151, 1181, 1229, 1279, 1319, 1399, 1471, 1549, 1669, 1709, 1789, 1831, 1861, 1879, 2039, 2069, 2111, 2221, 2269, 2309
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Discriminant = -520. See A139827 for more information.
|
|
LINKS
|
|
|
FORMULA
|
The primes are congruent to {5, 21, 31, 71, 109, 111, 119, 141, 149, 151, 189, 229, 239, 271, 279, 301, 319, 349, 359, 421, 431, 461, 479, 501, 509} (mod 520).
|
|
MATHEMATICA
|
QuadPrimes2[5, 0, 26, 10000] (* see A106856 *)
|
|
PROG
|
(Magma) [ p: p in PrimesUpTo(3000) | p mod 520 in {5, 21, 31, 71, 109, 111, 119, 141, 149, 151, 189, 229, 239, 271, 279, 301, 319, 349, 359, 421, 431, 461, 479, 501, 509}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\26), if(isprime(t=w+26*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|