In a letter to Leonhard Euler, dated 7 June 1742, Christian Goldbach, a not especially eminent mathematician, speculated that every even number greater than 2 was the sum of at least one pair of primes (a prime being an integer divisible solely by itself and 1). Thus 10 = 7+3, 32 = 13+19, 84 = 67+17, ad infinitum. To the great Euler, it probably seemed a trifling puzzle not worth racking his brain over…