With primitive polynomials, it's not too hard to get all the polynomials of a particular power. For example, columns in the following represent the 18, 16, 48, and 60 primitive polynomials of GF[2^7], GF[2^8], GF[2^9], and GF[2^10]:
You can also enter at the left, visit every white space, and exit at the right. It's a continuous connected cavern.
But here, I got lost in the caverns of GF[2^12]. I wasn't able to visit all the white spaces, and likely got eaten by a grue. Is there an optimal way to shuffle this set of primitive polynomial coefficients?
Here's more bad, dangerous caverns for all the primitive polynomials in caverns for powers 5 to 14.
Can the orderings of these primitive polynomials be made as safe as the solution for GF[2^7]-GF[2^10] at the top? Here are best found so for for GF[2^11] and GF[2^12]