Samuel Gross (Rocky Mountain College)
49598666989151226098104244512918
Let $f(x)$ be a polynomial with non-negative integer
coefficients for which $f(10)$ is a prime. A result of A. Cohn implies
that if the coefficients of $f(x)$ are $\le 9$,
then $f(x)$ is irreducible. In 1988,
M. Filaseta showed that the bound $9$ could be replaced
by $10^{30}$. Can we do better? We will answer this
question, discuss other numbers similar to the one in
the title of this talk, and explore some open problems related to our
recent work.