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It is a well known fact that almost all polynomials with integer coefficients and a nonzero constant term are irreducible over the rationals. Thus, given a polynomial $ f(x) \in\mathbb Z[x],$ one can naturally expect to fi nd an irreducible polynomial$ g(x) \in\mathbb Z[x]$ close to f(x) in the sense that the sum of the absolute values of the coffiecients of f(x)-g(x) is bounded by an absolute constant
C. This was proposed by Pal Turan during the 70's. Though the problem remains open, Andrzej Schinzel in 1970 and later Michael Filaseta and myself have been able to provide partial answers to
the problem. I shall discuss our result as well as a connection to another longstanding open problem from elementary number theory.
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