Question

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?​

Answer 1

Test the conjecture for 10 even numbers

10 = 3 + 7

12 = 5 + 7

14 = 7 + 7

16 = 5 + 11

18 = 5 + 13

20 = 7 + 13

22 = 11 + 11

24 = 11 + 13

26 = 13 + 13

28 = 11 + 17

Do you think the conjecture is true? Why or why not?

I believe the conjecture is true because the sum of two odd numbers is an even number and you can find two prime odd numbers for every even number whose sum is that even number.