How often are Lnα and Lnβ simultaneously primes?

Dixit, Anup B.

doi:10.1007/s11139-026-01373-x

How often are Lnα and Lnβ simultaneously primes?

2026-03-31

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DOI：10.1007/s11139-026-01373-x

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Abstract

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Let [x] denote the greatest integer less than or equal to a real number x. Given real numbers 0 < alpha(1) < alpha(2) < center dot center dot center dot< alpha(k) < 1 satisfying a certain condition, we show that there are infinitely many positive integers n for which all of [n(alpha 1)], [n(alpha 2)], ... , [n(alpha k) ] are prime numbers. Our approach relies on establishing a simultaneous equidistribution theorem for [n(alpha i)] across k-many arithmetic progressions.

Keywords:

Uniform distribution

Exponential sums

Prime distribution

How often are Lnα and Lnβ simultaneously primes?

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