We investigate the consecutive primes $p$ and $q$ ($p > q$) for which there exists a pair of natural numbers $(x,y)$ such that $p^x-q^y$ is a perfect square and make some conjectures.
On the Difference between Consecutive Primes and Estimates of the Number of Primes in the Interval $(n, 2n)$
On the difference between consecutive primes
On the gaps between consecutive primes
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