Like the elements in chemistry, prime numbers serve as building blocks in the mathematics of whole numbers. Evenly divisible only by themselves and one, primes are a rich source of speculative ideas that mathematicians often find simple to state but difficult to prove.
The Goldbach conjecture is a prime example of such a conundrum.
In a letter written in 1742 to Leonhard Euler (1707–1783), the historian and mathematician Christian Goldbach (1690–1764) expressed the belief that every integer greater than 5 is the sum of three primes. (See the letter at http://www.mathstat.dal.ca/~joerg/pic/g-letter.jpg and http://www.math.dartmouth.edu/~euler/correspondence/letters/OO0765.pdf.)