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The famous irreducibility criteria of Sch\"onemann-Eisenstein and Dumas relyon information on the divisibility of the coefficients of a polynomial by asingle prime number. In this paper we provide several irreducibility criteriaof Sch\"onemann-Eisenstein-Dumas-type for polynomials with integercoefficients, criteria that are given by some divisibility conditions for theircoefficients with respect to arbitrarily many prime numbers. A specialattention will be paid to those irreducibility criteria that requireinformation on the divisibility of the coefficients by two distinct primenumbers.

Sch\"onemann-Eisenstein-Dumas-type irreducibility conditions that use arbitrarily many prime numbers