Carmichael Numbers with Prime Numbers of Prime Factors
Thomas Wright

TL;DR
This paper proves, assuming Heath-Brown's conjecture, that infinitely many Carmichael numbers have a prime number of prime factors, advancing understanding of their distribution and properties.
Contribution
It establishes the infinitude of Carmichael numbers with a prime number of prime factors under a key conjecture, a novel result in number theory.
Findings
Infinitely many Carmichael numbers with prime number of prime factors are proven to exist.
The proof relies on Heath-Brown's conjecture on the first prime in an arithmetic progression.
The result links the structure of Carmichael numbers to prime distribution conjectures.
Abstract
Under the assumption of Heath-Brown's conjecture on the first prime in an arithmetic progression, we prove that there are infinitely many Carmichael numbers such that the number of prime factors of is prime.
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Taxonomy
TopicsAnalytic Number Theory Research · History and Theory of Mathematics · Advanced Mathematical Theories
