ABSTRACT
Before leaving the counting numbers some reference must now be made to what apart perhaps from Fermat’s Last Theorem is the most famous of all unsolved problems concerning the integers. It is unusually frustrating because this particular hypothesis can be stated in terms which are almost unbelievably simple. In an exchange of letters between Euler and the German mathematician Christian Goldbach in the year 1742, it is the suggestion that every even number can be written as the sum of two odd prime numbers. So persuasive is the numerical evidence from modern computer studies that hardly anyone really doubts the validity of the conjecture. Although not helping with regard to the Goldbach conjecture itself, a recent piece of computer investigation seems to suggest that all even numbers which are sufficiently large can even be expressed as the sum of two twin primes.
