Summary

  • The 2008 record prime received independent verification; establishing its exact numerical rank required a separate search through smaller candidates.
  • GIMPS reached that ranking milestone in April 2018, after years of repeat tests on results that usually said no.

At 12,978,189 digits, the number had no trouble making an entrance. Getting its place in line settled was a longer business.

GIMPS found 2^43,112,609 − 1 on 23 August 2008, on a UCLA computer managed by Edson Smith. It was then the largest known prime. The project's September announcement celebrated a discovery large enough to make ordinary numbers look underdressed. The computation had taken 34 days; independent checks followed using other programs and hardware.

There were two questions to answer. Was this enormous number prime? And exactly how many smaller Mersenne primes came before it? A Mersenne prime has the form 2^p − 1. Proving one candidate prime settles the first question. Settling its ordered position also requires confidence that the earlier search has missed none.

The dates tell the story. The official milestones record all smaller exponents tested at least once by 5 September 2012. Verification below this prime was completed on 8 April 2018, fixing its place as the 47th Mersenne prime. The project history lists two smaller discoveries made after the 2008 record, in September 2008 and June 2009. Discovery order and numerical order had different seating plans.

The patient second pass was part of the design. In their contemporary paper, George Woltman and Scott Kurowski describe first-time tests suffering an error rate of roughly 2%. Memory corruption, overheating and other hardware troubles could intrude on long calculations. A theorem might be dependable; the desktop executing it still had a fan.

New primes received immediate checks by third parties with different hardware and software. For candidates reported composite, limited resources meant rerunning the test with the same software. The system compared the last 64 bits of the results. A random shift at the start changed the data handled by the calculation, helping guard against a software bug reproducing the same answer. Repetition had to be designed, too.

The internet made this a manageable shared workload. A central server assigned work, clients calculated and returned results, and progress reports and team tables gave participants something to follow. The quieter contribution was to return another well-checked negative result. Each such result helped close the gap behind the search frontier. The giant prime had its discovery day in 2008; its settled place in the list also belonged to the people who kept doing the arithmetic after the applause.