brocard

The code in this repository was used in an attempt to find more solutions to Brocard's problem.

Up until now, only the first 1x10^12 (1 trillion) numbers have been tested in an attempt to find an additional solution. One of our primary goals was to increase the amount of values tested by three orders of magnitude.

• A non-overclocked Threadripper 3970x (32 cores, 64 threads) was used to run this application.

Prerequisites

• flint2
• GMP
• Celero (optional, to run benchmarks)
• gtest (optional, to run mulmod test)

Findings

We tested the first 1x10^15 (1 quadrillion) values over a period of ~5 months (January-May, 2020), but no additional solutions were found.

We used a similar algorithm to the one described in this paper, but added additional optimizations (short-circuiting, Zen2 architecture-friendly code, etc.)

The number which passed the most tests (49/50) was 602,723,832,772,967.

• The odds of finding another number that passes that many tests is 1 in 500 trillion.