Pith. sign in

REVIEW 1 cited by

Mills' constant is irrational

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2404.19461 v2 pith:MPHMJHBY submitted 2024-04-30 math.NT

Kota Saito This is my paper · ORCID
classification math.NT
keywords numbermillsconstantirrationalintegerlfloorrealrfloor
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

Let $ \lfloor x \rfloor $ denote the integer part of $ x $. In 1947, Mills constructed a real number $ \xi > 1 $ such that $\lfloor \xi^{3^k} \rfloor$ is always a prime number for every positive integer $k$. We define Mills' constant as the smallest real number $\xi$ satisfying this property. Determining whether this number is irrational has been a long-standing problem. In this paper, we show that Mills' constant is irrational. Furthermore, we obtain partial results on the transcendency of this number.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Intervals without primes near an iterated linear recurrence sequence

    math.NT 2025-04 accept novelty 5.0 of 10

    Iterated reversible linear recurrences have infinitely many prime-free windows of width roughly log n/(2D), which also makes many floor values of Pisot and Salem powers composite.

Pith tools