Fermat's Enigma

by Simon Singh

all other numbers can be created by multiplying combinations of the prime numbers. This seems to lead to a remarkable breakthrough. To prove Fermat’s Last Theorem for all values of n, one merely has to prove it for the prime values of n. All other cases are merely multiples of the prime cases and would be proved implicitly. Intuitively this enormously simplifies the problem, because you can ignore those equations that involve a value of n that is not a prime number. The number of equations remaining is now vastly reduced. For example, for the values of n up to 20, there are only six values that need to be proved: If one can prove Fermat’s Last Theorem for just the prime values of n, then the theorem is proved for all values of n. If one considers all whole numbers, then it is obvious that there are infinitely many. If one considers just the prime numbers, which are only a small fraction of all the whole numbers, then surely the problem is much simpler?