(updated 20230517)

The last logs (153. 500000 is maximal, 154. w32 "Just in case",  155. More candidates and 741454) have shaken a few misconceptions and hopes, and this log summarises the current situation.

Binary PEAC

The old well known widths have not changed : 2, 3, 4, 10, 16 and 26 bits. The perfection of w26 is interesting to examine but not a critical issue.

w32 is now out of the race.

w31 failed too because 2147483648 % 7559=1984.

w30 still passes the sieve.

Even larger widths (51 52 54 55 59 60 and 63 passed the current sieve_1M) might not be testable in the near future.

gPEAC

2^(29/2) = 23170 is known perfect and fits in a pair of 15-bit registers. it's suitable for small systems, small data, with its 500M orbit.

2^(39/2)-1 = 741454 is known perfect, using 19-bit registers. It's a direct upgrade for PEAC16 with its longer orbit (549.754.775.568) and great mixing (10110101000001001110). It's appropriate for 16-bit scramblers, hash tables, checksums, and the 3 extra bits (compared to PEAC16) add even more robustness.

Other candidates have not been found. Many have failed a quick scan/check in seconds or minutes, up to 77.