# Counterexamples to the Baillie-PSW primality test

**Problem (1)**Find a counterexample to Baillie-PSW primality test or prove that there is no one.

**Problem (2)**Find a composite or which divides both (see Fermat pseudoprime) and the Fibonacci number (see Lucas pseudoprime), or prove that there is no such .

Selfridge, Wagstaff, and Pomerance offered $500 + $100 + $20 for satisfying Problem 2, and $20 + $100 + $500 for a proof that there is no such (R. Guy, 1994).

## Bibliography

Carl Pomerance. "Are There Counterexamples to the Baillie-PSW Primality Test?"

Thomas R. Nicely. " The Baillie-PSW primality test."

R. K. Guy. "Pseudoprimes. Euler Pseudoprimes. Strong Pseudoprimes". §A12 in "Unsolved Problems in Number Theory", 2nd ed. New York: Springer-Verlag, pp. 27-30, 1994.

* indicates original appearance(s) of problem.