49598666989151226098104244512918

Let f(x) be a polynomial with non-negative integer coefficients for which f(10) is prime. A result of A. Cohn implies that if the coefficients of f(x) are ⩽9, then f(x) is irreducible. In 1988, the first author showed that the bound 9 could be replaced by 1030. We show here that the bound 9 can be replaced by the number in the title and that this is the largest integer with this property. Other related results are established.