A325870 Primes represented by non-quadratic cyclotomic binary forms.

11, 13, 17, 31, 43, 61, 73, 97, 127, 151, 181, 193, 211, 241, 257, 331, 337, 421, 461, 463, 521, 541, 547, 577, 601, 641, 683, 757, 881, 991, 1009, 1021, 1031, 1093, 1297, 1621, 1801, 1871, 1873, 1933, 2221, 2417, 2657, 2731, 2801, 3001, 3121, 3361, 3571, 3697

Offset: 1

Author

Peter Luschny, May 26 2019

Keywords

• nonn

Links

• Peter Luschny, Table of n, a(n) for n = 1..185
• Étienne Fouvry, Claude Levesque, and Michel Waldschmidt, Representation of integers by cyclotomic binary forms, arXiv:1712.09019 [math.NT], 2017 and Acta Arithmetica, online 15 March 2018.

Crossrefs

Cf. A296095, A293654, A325143, A325145.

Programs

PARI

isA325870(n) =
{
    my(K, M, phi);
    K = floor(5.383*log(n)^1.161);
    M = floor(2*sqrt(n/3));
    for(k = 3, K,
        phi = eulerphi(k);
        if(phi >= 4,
            for(y = 1, M,
                for(x = y + 1, M,
                    if(n == y^phi*polcyclo(k, x/y),
                        return(1)
    )))));
    return(0)
}

Extensions

At the suggestion of Michel Waldschmidt