Question: Pierre de Fermat (16011665) conjectured that the function f (x) = 2 (2x) + 1 for x = 1, 2, 3, . . . ,

Pierre de Fermat (1601–1665) conjectured that the function f (x) = 2^(2x) + 1 for x = 1, 2, 3, . . . , would always have a value equal to a prime number. But Leonhard Euler (1707–1783) showed that this formula fails for x = 5. Use a calculator to determine the prime numbers produced by f for x = 1, 2, 3, 4. Then show that f (5) = 641 × 6, 700,417, which is not prime.

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