Mathematical Projects

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The subject of mathematics currently utilizes distributed computing the most. There are numerous mathematical projects that are currently running or have already been completed, like the aforementioned Great Internet Mersenne Prime Search and the Optimal Golomb Ruler Search. The number of mathematics-related projects outweigh scientific research because it is easier to create a program that solves purely mathematical problems, as opposed to cracking a more scientific problem that involves complex sets of dependent variables.

finding the bits of Pi

 Fig. 1: PiHex website www.cecm.sfu.ca/projects/pihex/pihex.html

The PiHex project was one of the first successful distributed computing projects on the internet. To date, the PiHex project has discovered that the five trillionth and forty trillionth bits of pi are 0, in Hexadecimal format. The first calculation took a short five months with only 25 computers running the software.

A bit of pi is different than typical numbers, though. The five trillionth number of pi isn't 0, but the bit is. PiHex utilizes the Bailey-Borwein-Plouffe algorithm, which allows one to calculate the dth digit of pi without calculating the d - 1 digits. (Finch) This algorithm lends itself well to distributed computing since ranges of calculations can be assigned. The formula, however, gives answers in base 16 — numbers that are not based on the number 10 which we are familiar with. Whereas typical numbers have ten distinct digits, from zero to nine, numbers with a base of 16 have sixteen digits; they start at zero and go through nine, then use the first six letters of the alphabet. Still, even the five-trillionth bit calculation is quite a feat when compared to the previous pi-bit record of a mere one trillionth bit.

 With over 500 computers currently working on the project, PiHex's last goal — to find the quadrillionth bit of pi — is becoming a reality. This PiHex project should have been completed earlier, but the client isn't very complex, and the user must set up some things manually. That leaves room for error: the PiHex project was set back because some users accidentally deleted data from a log that they shouldn't have, and other users encountered overheated computer problems, which returned the data to the PiHex server with errors. (Percival) Fig. 2: Bits: Mathematical as well as cryptography projects can utilize them.

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