Look at the logs
155. More candidates and 741454
156. The good numbers
163. Hash enhancements

The scan has harvested a very interesting number:

• m= 2^(39/2)-1 = 741454 = 2×7×211×251 = 10110101000001001110b is known perfect, using 20-bit registers.
• orbit = 549.754.775.568 = 111111111111111111100000010100000010000 in binary, takes about 8 minutes to scan.
• offset: o = 0111.11010101.11010101 = 7D5D5h = 513493 = 107×4799

With these parameters, we get a very effective hash algorithm for text strings, 2 bytes at a time (among others). Aside from the PEAC structure itself and its Fibonacci/Pisano scrambling with the addition,

• The modulus is conditional and increases the scrambling by seeding avalanche with 8 more bits,
• The offset is unconditional and increases the avalanche in normal ASCII characters, while also triggering "End Around Carry" much more often than normally with empty input.

TODO

• Check common divisors of 741454 | 513493 : none !
• Check the orbit length of PRNG with offset 513493

For this, the "scanner" must be modified to add the offset, which creates all kinds of ... hmmm algorithmic questions. Fortunately there are two ways to design a checksum with PEAC : single-carry or dual-carry. Single-carry is less parallel but uses a bit fewer operations. It's easy to adapt with the binary PEAC but I realise it's the first time I do this operation on a gPEAC: it's my first gPEAC checksum.

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