There are long runs of reducible polynomials over GF(p) for particular p and degrees. The routine gfip here searches for irreducible polynomials (IPs) simplest first, or lexicographically. When seeking an IP for GF(6700417⁵) it seems to stall. For n < 5, GF(6700417ⁿ) has dense IPs of the form xⁿ+k. It turns out that there are very few if any IP's of the form x⁵+k which the routine is programmed to exhaust before considering anything else. Searching the entire set of 6700417⁵ monic polynomials over GF(6700417) randomly yields frequent IPs. There are even abundant k's for which x⁵+x+k is irreducible. There are many k's for which x⁵+k is irreducible over GF(641) but not over GF(6700417). There is a pattern here that needs a theory.