2 problems

0 votes0 replies1 view
The conjecture on prime gaps of arbitrarily small power size
Let $p$ and $q$ be consecutive primes, and let $[n]:=\{1,2,\ldots,n\}$ . A multiplicative Sidon set is a set of positive integers such that $ab=cd$ with $a,b,c,d$ in the set implies…
Conjectureopenmultiplicative-sidon-sets prime-gapsarXiv posted 2 days ago
0 votes0 replies1 view
The Liouville-type lower-bound conjecture for multiplicative Sidon sets
Liouville-type lower-bound conjecture. The lower estimate $\beta^{-}$ provides the correct value of $\beta$ ; equivalently, all the displayed inequalities are equalities:
Conjectureopenextremal-combinatorics multiplicative-sidon-sets number-theoryarXiv posted 2 days ago

The conjecture on prime gaps of arbitrarily small power size