|
|
A244146
|
|
Primes of the form x^2 + x*y + y^2 with x, y primes.
|
|
4
|
|
|
19, 67, 79, 109, 163, 199, 349, 433, 457, 607, 691, 739, 937, 997, 1063, 1093, 1327, 1423, 1447, 1489, 1579, 1753, 1777, 1987, 2017, 2089, 2203, 2287, 2383, 2749, 3229, 3463, 3847, 3943, 4051, 4177, 4513, 4567, 5347, 5413, 5479, 5557, 5653, 6079, 6133, 6271, 6661
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Equally: primes that are of the form (p+q)^2 - p*q, with p, q primes. - Antti Karttunen, Jun 21 2014
|
|
LINKS
|
|
|
EXAMPLE
|
The terms 19, 67, 79 and 1777753 are in the sequence because they can be represented as:
19 = 2^2 + 2*3 + 3^2 = (2+3)^2 - 2*3.
67 = 2^2 + 2*7 + 7^2 = (2+7)^2 - 2*7.
79 = 3^2 + 3*7 + 7^2 = (3+7)^2 - 3*7.
1777753 = 677^2 + 677*859 + 859^2 = (677+859)^2 - 677*859.
|
|
MATHEMATICA
|
Reap[For[p = 2, p < 10^4, p = NextPrime[p], If[Reduce[p == x^2 + x y + y^2, {x, y}, Primes] =!= False, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Jul 12 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|