This repository contains convergence sieves for the verification of the Collatz problem.
To understand the *.map
files, see the detailed description on the Wikipedia page.
For example, the 16 least-significant bits of a number n
can be used as bit-index into the esieve-16.map
.
This result is that only 1720 out of 65536 numbers (about 2.6 %) must be checked for convergence.
I have found that these convergence sieves (considering values stored in bits) have a kind of internal structure. Specifically, sieves are formed by only several constantly repeated 64-bit patterns, so I store only indices into a small look-up table.