Friday, May 27, 2022

A million-digit Leyland prime (reality check)

Having previously decided that finding a million-digit Leyland prime was doable and subsequently committing to a search thereof, it is time for a reality check.

The notion that I could scan the Leyland interval from L(999999,10) to L(1000099,10) by the end of September was predicated on an estimate of about 5 hours examination time per candidate (of some 59500 candidates). It turns out that the running time on my nine oldest Mac minis is closer to 11.5 hours and, for reasons I don't comprehend, three newer Mac minis are running at 18.5 hours per candidate. My 2020 iMacs, which I had assumed would be the most productive, still need 11 hours on my main machine (7 processes) and almost 15 hours on my helper machine (8 processes). I'm well into 2023 at this rate!

Early this morning Gabor Levai noted that he had discovered a 1000027-digit Leyland prime. Of my 108 running processes, this will have been found in about four months (by process #23 that happens to reside on one of the slower Mac minis). Disheartening, to say the least.

No comments:

Post a Comment