4 problems

Let $g(n)$ be Landau's function, and let $n1=1,n2=2,n3=3,n4=4,n5=5,n6=7, ldots$ be defined by … The gaps $n_{k+1}-n_k$ are known to have finite liminf. Landau's function liminf-gap…

Let $g(n)$ be Landau's function, and let $n_1=1,n_2=2,n_3=3,n_4=4,n_5=5,n_6=7,\ldots$ be defined by … The preceding results establish that the gaps $n_{k+1}-n_k$ are unbounded abov…

Nicolas's conjecture. There are infinitely many maximal increasing sequences with $k\geq2$. Such sequences are rare because of a parity phenomenon; the question of arbitrarily long…

Let $p_k$ be a prime, let $\Delta=\Delta(p_{k+1})$, and let $\delta_1(p_k)$ be the smallest even integer such that $\delta_1(p_k)\geq\Delta$ and … for…