... nor is there a predictable way of turning one up. Numerous formulae exist to calculate them, and a good many have been found already.

Have you a moderately-fast system, or perhaps a dual- or quad-core system? Download the software at PrimeGrid and while your system isn't playing a game or manipulating images in Photoshop or editing video in Premiere, it can be finding either factors for the prime equations or searching for the primes themselves.

Make sure to read the rules, download the BOINC client, study the troubleshooting guides if you experience problems, and ...

... REMEMBER: this is a processor-heavy series of calculations. Keep your computer where it'll receive plenty of cool, circulating air. Wouldn't want a hole in your tabletop or floor calculating a bunch of silly numbers, would you?