Further sieving on "one equation to rule them all"

This code is an attempt to extend the computations presented in 48 MORE SOLUTIONS OF MARTIN DAVIS'S QUATERNARY QUARTIC EQUATION. Using the cado-nfs implementation of the general number field sieve, I found that $A_{168}$ factors as a product including two primes equivalent to $5 \pmod 7$. By computing the recurrence relation mod every prime less than $10^9$ and using primefac's interface for the probabilistic elliptic-curve factorization method, all but $201$ of the remaining possibilities under $10000$ were eliminated, with only ${320,495,530,543,761,831,938}$ less than $1000$. Some interesting remaining numbers to look at are $1118$ and $3981$, since $A_{1118}$ and $B_{3981}$ are both prime. In addition, $(53^2-1)/2=1404$ is the smallest number not of the form $(p-1)/2$ which has not been eliminated ( $A_{26}|A_{1404}$ and $1214504828571031609765841B_{26}|B_{1404}$ is all that has been found ).