IdonealNumbers

Euler's 65 numeri idonei $1, 2, 3, 4, 5, …, 1848$ -- one class per genus of discriminant $-4n$ -- as an indexed collection of unknown count.

IdonealNumbersEuler's idoneal numbers, an indexed collection of unknown count.

Domain: Collections

Details

$Count(IdonealNumbers) = NaN$ : the 65 known idoneal numbers are exhaustive assuming the generalized Riemann hypothesis; unconditionally, at most one more (necessarily $> 1848$ ) could exist.
$At$ reads off Euler's table of 65; past it, returns unevaluated rather than asserting a completeness the field doesn't unconditionally have.
OEIS A000926. $n$ is idoneal iff every genus of binary quadratic forms of discriminant $-4n$ contains only one class -- equivalently, $n$ 's only representations $n = x^2 + m y^2$ (for each $m$ coprime to $n$ ) force $\gcd(x, y) = 1$ or similar; the list traces to Euler's search for primality-testing moduli.
Membership goes through Element: $Element(120, IdonealNumbers)$ is true, $Element(11, IdonealNumbers)$ is false.

Enumeration

1 more kept as data, checked against the oracles

About

Examples	1
Crosswalk	OEIS