6 - Intellectual Discovery

Summary

Friday – April 19, 1793

Is there anything more fascinating than prime numbers? The basic notion of prime numbers is so simple that even as a child I could understand it. Prime numbers cannot be written as a product, except of themselves and 1. For example 17, one of my favorite numbers, can only be written as 17 = 17 · 1 = 1 · 17, and that's all. However, prime numbers combine that beautiful simplicity with a mystifying nature and a profound meaning that only those who know and understand mathematics can appreciate. The prime numbers contain within them such mystery and intricacy that many problems remain unsolved after hundreds of years. Mathematicians conjecture about their nature; eventually some of those conjectures become theorems and are demonstrated, but other assertions remain unproved. For example, in 1742 Goldbach conjectured that every even number greater than 2 is the sum of two primes, but there is no proof of it and today this conjecture is unsolved.

Another intriguing characteristic of prime numbers is that although they seem so irregular as to appear to be random, one can also find a myriad of patterns just by arranging numbers in a certain way or by combining the prime numbers with some integers.

For example, the relation n² + n + 1 results in numbers that look like primes, but on close examination they are not.