9 problems

Let $q$ be a prime power and let $\textbf{F}_{q^n}$ be a finite field. Let $g\in\textbf{F}_{q^n}$ satisfy the conditions in Theorem, and suppose that $n\geq\log q$. Large-order con…

Let a positive integer $n$ be 2-good if $n-1$ has a prime factor $p$ satisfying … For an integer interval, let the numerator below count the 2-good primes in it and the denominator…

Let $n=am+1$, where $a$ and $m$ are positive integers, and let $p$ be the least prime divisor of $m$. Primality conjecture. If $a<p$ and $m\mid\phi(n)$, then $n$ is prime. This con…

A Baillie–PSW pseudoprime is an odd composite integer that passes both the strong probable-prime test and the Lucas primality test. Baillie–PSW pseudoprime infinitude conjecture. T…

Let $\lambda_n$ be the integer sequence considered in Theorem, and let $\mathfrak{F}$ be the divisor chosen on the genus-2 curve ${\mathcal H}:y^2=x^5+10$, namely…

Let $N$ be an odd composite number, and let the digital coding method be the divisor-finding procedure described in the paper. Write…

Let $N$ be an odd composite number, and let Algorithm 1 be the digital coding method for finding a divisor of $N$. Its iterations and its backtracking steps with a proper rule for…

Determinism conjecture. If

For each odd prime $p$, let $L_{p,3}$ denote the corresponding pseudocube, and let $q_n$ be the $n$th prime satisfying $q_n\equiv 1\ (\text{mod }3)$. Berrizbeitia–Müller–Williams c…