4 problems

McIntosh's conjecture. No prime $p$ satisfies this congruence.

Let $B_n(x)$ denote the Bernoulli polynomial of degree $n$, and let $p>3$ be prime. Sun's infinitude conjecture. There are infinitely many primes $p>3$ such that … The paper report…

Let $p>3$ be a prime, and let $E_{p-3}$ denote the Euler number of index $p-3$. A prime $p$ is called Euler-irregular in this setting when $E_{p-3}\equiv 0\pmod p$. Infinitude conj…

Let a Wall–Sun–Sun prime be a prime $p>5$ such that … where $\{F_n\}_{n\geqslant0}$ is the Fibonacci sequence and $(\frac p5)$ is the Jacobi symbol. The conjecture is that infinite…