Approximating number of irreducible polynomials over with several given coefficients

Irreducible polynomials have been studied since a long time. Due to their well known and promising role in different sciences, they have attained much importance. Here, we give formulae to calculate the approximate values which are close to the exact values for the number of irreducible polynomials over GF(p) of degree positive integer n≥r in which several coefficients, that is coefficients of x^n-1, …, x^n-r are given. We discuss the case r=4 in detail and state the approximated values in general case.