chapter  3
6 Pages

The World Record Holders

WithMalcolm E Lines

Although we know that the number of primes is infinite, there is nevertheless some recognition to be gained among the prime number fraternity from discovering the largest known prime at any particular moment in time. Nowadays, with powerful computers at our command, the associated fame tends to be fleeting, but before the advent of the electronic computer the fame was more permanent, and records sometimes stood for very long periods of time. The race has been going on for centuries and many mathematicians have striven to be part of it. Euler, in particular, held the record for well over one hundred years in the pencil and paper era. More recently the frequency of record breaking has accelerated considerably. Today the record rarely stands for more than a few years and sometimes for only a few days; just long enough to digest the next computer output. By this we do not wish to imply that no challenge is left for the aspiring record breaker or that programming a computer for an attack on the largest prime number pinnacle is easy. With a given computer the heights to which one can aspire are still a function of the efficiency of one’s method for checking for primeness, so that the challenge is certainly still there. On the other hand the research worker with the most powerful computer is certainly at an advantage. The complete list of prime number record holders since 1750, together with their respective primes, is shown in the accompanying Table 2.