A year of Development.

In 2014, we found Dario Aplern’s ECM factorization page. By 2018, we were using multiple instances to make the most of multi-core processors. This enabled us to run some processes in parallel, resulting in competitive factorizations.

Factorizations are measured by the magnitude of the largest co-factor: the relevant number is the second largest factor, not simply the biggest part of the factorization. This is because a small factor takes very little processing to discover. On the other hand, the large portion evacuates as prime by a statistical test. The task is only difficult if unfactored portion is composite. The computer has to check numbers up to the square root of the biggest factor. This is only difficult if the biggest factor (called a “co-factor,” in technical terms) is also large.