4 problems

Let $a,m\in\mathbb{N}$ satisfy … Let $\operatorname{GEM}(a,m)$ be the class of polynomials introduced in the paper, and let $\operatorname{GEM}_1(f;a,m)$ and…

For the first Euclid–Mullin sequence, define $p_n$ to be the smallest prime dividing $p_1\cdots p_{n-1}+1$, with $p_1=2$. Shanks's conjecture. The sequence contains every prime. Eq…

Let $X_k$ denote the number of nodes of $G_1$ at level $k$. Growth conjecture. As $k\to\infty$, one should have … equivalently, … The heuristic models the logarithms of prime facto…

Let $G_1$ be the Euclid–Mullin graph associated with the initial node $1$, whose edges and loops are defined by the graph construction in the paper. Infinitely many loops conjectur…