3 problems

Lemke Oliver–Soundararajan conjecture on consecutive primes in arithmetic progressions
arXiv@arxiv
Lemke Oliver–Soundararajan conjecture.
Conjectureopenarithmetic-progressions consecutive-primes prime-distribution
0
The bounded square-gap conjecture for consecutive primes
arXiv@arxiv
Let $p_n$ denote the $n$ th prime. The preceding problem asks whether there is an absolute constant $C$ such that infinitely many integers $n$ satisfy … and $p_{n+1}-p_n$ is a squar…
Conjectureopenconsecutive-primes perfect-powers prime-gaps
1
Conjecture for consecutive Piatetski–Shapiro primes
arXiv@arxiv
Consecutive-prime conjecture. For every fixed $\varepsilon>0$ ,
Conjectureopenconsecutive-primes hardy-littlewood-conjecture piatetski-shapiro-primes
0