Geodesic
Bounded gaps between primes of special form
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 75-78

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Let $0\alpha$, $\sigma1$ be arbitrary fixed constants, let $q_1$ be the set of primes satisfying the condition $\{q_n^\alpha\}\sigma$ and indexed in ascending order, and let $m\ge1$ be any fixed integer. Using an analogue of the Bombieri–Vinogradov theorem for the above set of primes, upper bounds are obtained for the constants $c(m)$ such that the inequality $q_{n+m}-q_n\le c(m)$ holds for infinitely many $n$.
Keywords: consecutive primes, small gaps, fractional parts, bounded gaps, sieve method, Bombieri–Vinogradov theorem. 
A. V. Shubin. Bounded gaps between primes of special form. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 75-78. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a15/
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