PRIMABOINCA

**Project Summary** PRIMABOINCA is a research project that uses Internet-connected computers to search for a counterexample to some conjectures.

This project concerns itself with two hypotheses in number theory. Both are conjectures for the identification of prime numbers. The first conjecture

Agrawal’s Conjecture) was the basis for the formulation of the first deterministic prime test algorithm in polynomial time (AKS algorithm). Hendrik Lenstras and Carl Pomerances heuristic for this conjecture suggests that there must be an infinite number of counterexamples. So far, however, no counterexamples are known. This hypothesis was tested for n < 1010 without having found a counterexample. The second conjecture

(Popovych’s conjecture) adds a further condition to Agrawals conjecture and therefore logically strengthens the conjecture. If this hypothesis would be correct, the time of a deterministic prime test could be reduced from O(log N)6 (currently most efficient version of the AKS algorithm) to O(log N)3.

**Applications**Linux/x86

Windows/x86

Cell BE

Mac OS 10.4+ running on an Intel CPU

**Connecting to PRIMABOINCA**The projects Home Page is located at:

http://www.primaboinca.com/PRIMABOINCA is listed as a project in BOINC and the various BOINC Account Managers for direct connection.

Following your registration don't forget to join BOINC@Australia Team by following the directions on the Home Page.

**Statistics**View or Team Members List and their current score:

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