Prime Number Search

[ttw]

That recursion is much faster, but the memory grows linearly. I run about 10,000 steps/minute in my latest ranges (about 112 to 127 bits). Without storage, the depth recursion is somewhere about 140 steps. About half the mods have zero for the quotient which helps. I did have a recursion formula for the mod function but it got a bit complicated. That's why I used the limited context formula.

The other big advantage is that the sum of partial quotients in S(i)/S(i+1) is constant. This gives good parameters for a linear congruential pseudo-random number generator. One doesn't need to search for a "good" multiplier. I need to look further, but the ordering seems to come from taking the partial quotients and combining two (or maybe more) early quotients to get the next term. There may be a useful procedure from this.

It's a nice sequence. The Stern-Brocot tree and the Calkin-Wilf tree can be derived from the sequence. Also Minkowski's ? function. It provides a 1-1 mapping from rationals to integers.

I'll post some of the code later. I cannot get the computers to speak to the EMU48 program for some reason. I am re-creating a high-speed Fortran code for multiple precision integers that I used to use. Then I can run these on a PC (which I tested as at least 1000x the EMU48.) It's just a hobby.