# Lecture 5: Finding Large Primes - Mersenne Primmes

### Background Material

- Geometric Series - 1 + x + ... + x^n = (x^(n+1)-1)/(x-1) if x &ne 0.

### Reading

### Topics

- Euclid's proof that there are infinitely many primes.
- Proof that there are infinitely large gaps between consecutive primes.
- Perfect numbers and Mersenne primes.
- Lucas-Lehmer algorithm - need for arbitrary precision integer
arithmetic and fast integer multiplication.

### Slides and Lecture Notes

- infprimes.pdf - hand written notes from the lecture.

### Maple worksheets and other resources

Created: April 14, 2008 by
jjohnson AT cs DOT drexel DOT edu