A peculiarity of Eisenstein polynomials

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I've tested polynomials of degree 6 with random integer coefficients $|a_i|<50$ in test-series of $10,000$. The probability of a random primitive polynomial of the kind to be reducible seems to be a little more than $2 \%$.

For sums of three random irreducible polynomials, primitive sum or not, the probability of being reducible also seems more than $2 \%$.

However, for sums of three random Eisenstein polynomials, primitive sum or not, the probability of being reducible seems less than $1 \%$.

Other degrees and limits for the coefficients gives just about the same results.

How to explain this property of this class of polynomials?

Hint? A perhaps even more peculiar property is that for the sum of two Eisenstein polynomials, the probability of being reducible is about $70 \%$! While corresponding test for two random irreducible polynomials gives about $2 \%$ reducible.

The main reason why sums of two Eisenstein polynomials has high probability of being reducible seems to be that all coefficients tends to be even. When such a sum is divided with the greatest common divisor about $5\%$ are reducible.

Using an Eisenstein polynomial twice, getting polynomials of the form $2p+q$ gives about $1.3 \%$ reducible.


A random Eisenstein polynomial is here a random polynomial of degree 6 divided with the greatest common divisor of the coefficients, which is selected if it satisfies the Eisenstein criteria. And similar for a random irreducible polynomial. Just brutal force trial and error.