4 problems

Let $b$ be an integer such that $-b$ is not an integer square, and define … Natural-density conjecture. As $x$ tends to infinity, … This would identify the natural density of indic…

Let $\beta$ be a nonzero integer and define the sequence $P=(P_n)$ by … A term $P_n$ has a primitive divisor if it has a prime divisor that divides no earlier nonzero term of the s…

For each positive integer $i$, consider the integer $2^i-3$. A primitive prime divisor of $2^d-3$ is a prime divisor that divides none of the earlier terms $2^i-3$ with $i<d$. Prim…

Primitive divisor conjecture. The term $a_n$ has a primitive prime divisor for all but finitely many $n$. Moreover, there exists a positive integer $M$ such that, whenever $a_n$ do…