Assumptions:
TeX:
g_{p} = \begin{cases} 10, & p = 40487\\7, & p = 6692367337\\\min\left(A\right), & \text{otherwise}\\ \end{cases}\; \text{ where } A = \left\{ a : a \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \# \left\{ {a}^{k} \bmod p : k \in \mathbb{Z}_{\ge 0} \right\} = p - 1 \right\} p \in \mathbb{P} \;\mathbin{\operatorname{and}}\; p \ge 3 \;\mathbin{\operatorname{and}}\; p < {10}^{12}
Definitions:
Fungrim symbol | Notation | Short description |
---|---|---|
ConreyGenerator | Conrey generator | |
Minimum | Minimum value of a set or function | |
ZZGreaterEqual | Integers greater than or equal to n | |
Cardinality | Set cardinality | |
Pow | Power | |
PP | Prime numbers |
Source code for this entry:
Entry(ID("540931"), Formula(Where(Equal(ConreyGenerator(p), Cases(Tuple(10, Equal(p, 40487)), Tuple(7, Equal(p, 6692367337)), Tuple(Minimum(A), Otherwise))), Equal(A, Set(a, For(a), And(Element(a, ZZGreaterEqual(1)), Equal(Cardinality(Set(Mod(Pow(a, k), p), For(k), Element(k, ZZGreaterEqual(0)))), Sub(p, 1))))))), Variables(p), Assumptions(And(Element(p, PP), GreaterEqual(p, 3), Less(p, Pow(10, 12)))))