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?