Wednesday, January 25, 2023

A million-digit Leyland prime (end of run)

manual distribution worksheet for 59536 primality tests
An hour ago I completed the primality check of 59536 Leyland-prime candidates that I started on 2 May 2022. My 27 May 2022 reality check explains why it took way longer (just short of nine months) than I had originally planned. Preceding the primality testing was another month (or so) sieving the original Leyland numbers file (so as to exclude divisibility by primes up to 2*10^11), so ten months altogether, now done.

What have I discovered? Of Leyland numbers with at least one million decimal digits, but fewer than one million one hundred decimal digits, there is only one prime. That prime was discovered by Gabor Levai long before I got to it. I saved all of my primality-test output where the 59536 entries are listed smallest to largest. If you want to see the one prime, search for "PRP".

The execution times vary wildly (due to processor circumstances) with an average of 9.45 hours per test. That would work out to 64 years if I hadn't been able to multi-process. I know now how to keep the execution times to 6 hours or less per test but that means running fewer processes per machine. Still, I might be able to shave a couple of months off the total time required for the next run.

No comments:

Post a Comment