67. The Goldbach Conjecture. Recall that a prime number is a
natural number whose only factors are itself and 1 (examples
of primes are 2, 3, 5, 7, and 11). The Goldbach conjecture,
posed in 1742, claims that every even number greater than
2 can be expressed as the sum of two primes. For example,
4 = 2 + 2,6 = 3 + 3, and 8 = 5 + 3. A deductive proof
of this conjecture has never been found. Test the conjecture
for at least 10 even numbers, and present an inductive argu-
ment for its truth. Do you think the conjecture is true? Why
or why not?​