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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
Sequence in context: A191023 A078861 A106891 * A106890 A048058 A048059
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, May 24 2011
STATUS
approved

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Last modified June 18 17:16 EDT 2024. Contains 373482 sequences. (Running on oeis4.)