The recent sieving effort has not yet slashed the hope that w32 be perfect or maximal. The sieve can only tell if a modulus is not either of them but the required amount of sieving makes the sieve almost as large as the number to be even 1/2 accurate.

But since the possibility is not ruled out so far, the chances are still good that it might be. And considering the amounts of time involved in this research, it could be worth it to have at least a "try": it would be good to start mapping its structure, even partially. In 2 years, I have not even considered scanning the primary orbit, it could be short and that would be the end of it !

[yg@localhost gPEAC_500K]$ /usr/bin/time ./gPEAC_scan 4294967296 4294967296
4294967296 M
1 candidates among 1 numbers (100.00000%)
1 hits among 1 candidates (100.00000%)
17.18user 0.00system 0:17.21elapsed 99%CPU
[yg@localhost gPEAC_500K]$ 

OK... sigh... The scanner says it's maximal but only lasts 17 seconds ? Time for more investigation.

.

.

Aaaaaand it seems that it is caused by an overflow in the computation of the orbit length... No wonder it stops early. Or maybe that's just the case that w32's primary orbit's length is 13.603.546.275 only :-/ So this case is closed after 2 years. Let's now look at the other possible orbits (those that the sieve has not ruled out):

• w30 hasn't stopped in 27 hours. But it's less interesting than w31.
• w31 didn't stop after 24 hours. That would be interesting to investigate, right ? The sign bit could be used instead of the carry bit, as a lesser replacement for w32: it would not be able to hash 32-bit numbers though :-/
• w34 stopped in 2m31s after 118.781.994.407 iterations.
• w35 took only 20s with 15.959.149.451 iterations
• w40 looks barely stronger with 8803509994715 iterations in 15800s/4h39m

How is it possible to be this unfortunate ?

Time to reconsider the goals. Let's see if w31 is really worthy more efforts.

Fortunately, there is a hit with sqrt(2^39)