## About primaboinca

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 < 10^{10}
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}.

You can participate by downloading and running a free program on your computer.

## Join primaboinca

- Read our rules and policies
- This project uses BOINC. If you're already running BOINC, select Attach to Project. If not, download BOINC.
- When prompted, enter
**http://www.primaboinca.com/** - If you're running a command-line or pre-5.0 version of BOINC, create an account first.
- If you have any problems, get help here.

## Returning participants

- Your account - view stats, modify preferences
- Teams - create or join a team
- Certificate
- Applications