T-Fermat integers

Tigran Hakobyan

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arXiv · 2603.00679

T-Fermat integers

Tigran Hakobyan

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Abstract

We introduce the concept of a T-Fermat integer, which generalizes the notion of a prime number. We show that any composite T-Fermat integer, if one exists, must be a Carmichael number. We prove several properties of T-Fermat integers and conjecture that there are infinitely many composite T-Fermat integers. Together with a further structural conjecture, this suggests a possible route toward proving the infinitude of primes $p$ such that $\omega(p-1)\leq 2$.

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Tigran Hakobyan. 2026-02-28. T-Fermat integers. https://arxiv.org/abs/2603.00679

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