A191031 Primes that are squares mod 43.

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

Offset: 1

Author

T. D. Noe, May 24 2011

Keywords

• nonn
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[p: p in PrimesUpTo(569) | JacobiSymbol(p,43) eq 1]; // Vincenzo Librandi, Sep 10 2012

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#, 43] == 1 &]

PARI

isok(n) = isprime(n) && issquare(Mod(n, 43)); \\ Michel Marcus, Apr 15 2018