Pierre de Fermat (16011665) conjectured that the function f(x) = 2(2) + 1

Pierre de Fermat (1601€“1665) conjectured that the function

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(S) = 641 × 6,700,417, which is not prime.

f(x) = 2(2") + 1