Agoh's conjecture: its generalizations, its analogues

TL;DR

This paper explores generalizations and analogues of Agoh's conjecture, proposing new conjectures involving prime-related congruences and combinatorial objects to understand prime generation and properties.

Contribution

It introduces two new generalizations of Agoh's conjecture and formulates conjectures involving prime-related congruences and combinatorial objects.

Findings

Proposed new generalizations of Agoh's conjecture

Formulated conjectures on prime-related congruences involving special functions

Thesis on combinatorial objects avoiding fake primes

Abstract

In this paper we formulate two generalizations of Agoh's conjecture. We also formulate conjectures involving congruence modulo primes about hyperbolic secant, hyperbolic tangent, N\"orlund numbers, as well as about coefficients of expansions in powers of other analytic functions. We formulate a thesis about combinatorial objects that do not produce fake primes.