9 problems

Let $\mathbb{P}$ denote the primes, let $i\in\{1,2\}$, and let $C_i[p]$ be the Cunningham chain associated with $p$. The logarithmic Cunningham-chain bound. For every prime $p>5$,…

The rogue divisor conjecture. The least prime divisor of $k$ is smaller than $p$:

Let $\mathbb{P}$ denote the primes, let $i\in\{1,2\}$, and let $\operatorname{Rog}(\mathbb{P})$ be the set of rogue primes. For a rogue prime $q$, let…

A Cunningham chain is a finite sequence of primes of the form $\{p,2p+1,4p+3,\ldots,2^{n-1}(p+1)-1\}$. The arbitrarily long Cunningham chains conjecture. There are arbitrarily larg…

Let $l(p)$ be the length of the Cunningham chain generated by the prime $p$, and let $\mathbb P$ denote the set of primes. Cunningham-chain length conjecture. On the primes, … Equi…

Caldwell's conjecture. The number of primes $p\leq N$ with $l(p)\geq k$ satisfies

Cunningham chain conjecture. The number of Cunningham chains of length $k$ beginning with a prime $p\leq N$ is approximately

Jones's polynomial Cunningham-chain reducibility conjecture. The polynomial is reducible over $\mathbb{Q}$ if and only if $j=t$. This conjecture proposes an explicit family of init…

Let $\epsilon\in\{-1,1\}$. A Cunningham chain is a sequence of prime numbers $p_1,p_2,p_3,\ldots$ satisfying $p_i=2p_{i-1}+\epsilon$ for all $i$; its kind is first or second accord…