The above prognostication was short-sighted. In fact, 48 perfect numbers have been discovered so far; the one mentioned above is only the eighth, and the prime indicated, 231−1, is not particularly large. As we saw in Chapter 15, even perfect numbers are in one-to-one correspondence with primes of the form 2p − 1. We also saw (in Chapter 7) that the question of which regular n-gons are constructible has to do with prime numbers of a certain form. Prime numbers are interesting in part because of their connections with famous problems such as these. In this chapter we discuss the ongoing search for large primes. How do we find large primes? Computers will be very useful in our calculations.