|
|
A139886
|
|
Primes of the form 10x^2 + 19y^2.
|
|
2
|
|
|
19, 29, 59, 109, 179, 181, 211, 269, 331, 379, 421, 509, 659, 661, 811, 829, 941, 971, 1019, 1021, 1091, 1171, 1181, 1229, 1291, 1381, 1459, 1549, 1571, 1579, 1699, 1709, 1741, 1789, 1861, 1931, 1979, 2029, 2131, 2141, 2179, 2269, 2309, 2339
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Discriminant = -760. See A139827 for more information.
10*x^2 + 19 produces 19 consecutive primes belonging to A028416 for x from 0 to 18. - Davide Rotondo, Jun 13 2022
Primes p such that Kronecker(2,p) <= 0, Kronecker(5,p) >= 0 and Kronecker(-19,p) <= 0. - Jianing Song, Jun 13 2022
|
|
LINKS
|
|
|
FORMULA
|
The primes are congruent to {19, 21, 29, 51, 59, 69, 91, 109, 141, 179, 181, 189, 211, 219, 221, 259, 261, 269, 299, 331, 341, 371, 379, 411, 421, 451, 459, 469, 509, 531, 611, 621, 629, 659, 661, 699, 749} (mod 760). [For the other direction, primes satisfying this congruence are terms of this sequence since 760 is a term in A003171. - Jianing Song, Jun 13 2022]
|
|
MATHEMATICA
|
QuadPrimes2[10, 0, 19, 10000] (* see A106856 *)
|
|
PROG
|
(Magma) [ p: p in PrimesUpTo(3000) | p mod 760 in {19, 21, 29, 51, 59, 69, 91, 109, 141, 179, 181, 189, 211, 219, 221, 259, 261, 269, 299, 331, 341, 371, 379, 411, 421, 451, 459, 469, 509, 531, 611, 621, 629, 659, 661, 699, 749}]; // Vincenzo Librandi, Jul 30 2012
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|