The Least Prime Number in a Beatty Sequence
J\"orn Steuding, Marc Technau
TL;DR
This paper establishes an upper bound for the smallest prime in an irrational Beatty sequence, drawing parallels with Linnik's theorem on primes in arithmetic progressions, advancing understanding of prime distribution in such sequences.
Contribution
It provides the first known upper bound for the least prime in irrational Beatty sequences, extending prime distribution results to this setting.
Findings
Upper bound for least prime in irrational Beatty sequences
Comparison with Linnik's theorem on arithmetic progressions
Advancement in understanding prime distribution in non-linear sequences
Abstract
We prove an upper bound for the least prime in an irrational Beatty sequence. This result may be compared with Linnik's theorem on the least prime in an arithmetic progression.
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