A395590 Primes p such that Mordell's equation y^2 = x^3 - p^3 has at least 1 integral solutions with x > p.

7, 11, 23, 31, 47, 61, 157, 239, 271, 307, 397, 431, 661, 1151, 1259, 1487, 1549, 1759, 1951, 2063, 2243, 2551, 3671, 3709, 4357, 4799, 6011, 6287, 7351, 9397, 10303, 10799, 11689, 11903, 16691, 17209, 17471, 18371, 19927, 24527, 25261, 26927, 28559, 29399, 32051, 39983, 47137

Offset

1,1

Links

Zhining Yang, Table of n, a(n) for n = 1..118

XiaoYang Zhang, Within the range of P < 10^5, which primes P yield non-trivial solutions (x ≠ P) to the Modular equation y^2 = x^3 - P^3? (in Chinese).

Example

    P [x,y]
--------------------
    7 [8,13]
    7 [14,49]
    7 [28,147]
    7 [154,1911]
   11 [443,9324]
   23 [71,588]
   31 [155,1922]
   47 [74,549]
   61 [793,22326]
  157 [349,6216]
  239 [3649843439,220501401167040]

Prog

(Magma)
SetClassGroupBounds("GRH");
primes := [p : p in [2..400] | IsPrime(p)];
for k in primes do
    a := #IntegralPoints(EllipticCurve([0, 0, 0, 0, -k^3]));
    if a gt 1 then
        print k;
    end if;
end for;

Crossrefs

Cf. A081120.

Sequence in context: A372303 A255769 A175625 * A082496 A239733 A265768

Adjacent sequences: A395587 A395588 A395589 * A395591 A395592 A395593

Keyword

nonn

Author

Zhining Yang, Jun 03 2026

Status

approved