With the help of the file generated by the program described in the last log 147. C-ving, I was able to quickly write sieve.tgz and evaluate its ability to sieve out candidates, by comparing with the list of known interesting orbits. It's good but it still misses quite a lot...

[yg@localhost sieve]$ for num in $(seq 13 10000); do
   ./gPEACsieve $num && echo OK $num
done |grep OK > 10000.out
[yg@localhost sieve]$ wc -l 10000.out 
2543 10000.out

So 3/4th of the integers have been sieved out, when there are 1384 orbits below 10000 that are perfect or maximal.

Pushing to 131540, we get 34495 unsieved candidates, almost 2.5× more than the 13646 from the original list. As the numbers increase, the sieve becomes less and less efficient, hence the need of a more thorough scan to build a better sieve.

Given the numbers already collected, I might be able to analyse why so many numbers are missed by the sieve, but the existing code is already enough to create a standalone function to assist the scanner, as planned.