|
|
A191031
|
|
Primes that are squares mod 43.
|
|
2
|
|
|
11, 13, 17, 23, 31, 41, 47, 53, 59, 67, 79, 83, 97, 101, 103, 107, 109, 127, 139, 167, 173, 181, 193, 197, 229, 239, 251, 269, 271, 281, 283, 293, 307, 311, 317, 337, 353, 359, 367, 379, 397, 401, 431, 439, 443, 461, 479, 487, 509, 541, 547, 557, 563, 569
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
These primes split in O_(Q(sqrt(-43))) (note that 43 ramifies, since it's divisible by -43). For the primes p listed here that are less than 43, note that 4p = 43 + x^2. For example, 4 * 13 = 52 = 43 + 3^2, 4 * 17 = 68 = 43 + 5^2. - Alonso del Arte, Apr 03 2018
|
|
LINKS
|
|
|
MATHEMATICA
|
Select[Prime[Range[200]], JacobiSymbol[#, 43] == 1 &]
|
|
PROG
|
(Magma) [p: p in PrimesUpTo(569) | JacobiSymbol(p, 43) eq 1]; // Vincenzo Librandi, Sep 10 2012
(PARI) isok(n) = isprime(n) && issquare(Mod(n, 43)); \\ Michel Marcus, Apr 15 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|