In 1742 the mathematician Christian Goldbach observed that every even number (except 2) seemed representable as the sum of two primes. Goldbach could not prove this result, known today as Goldbach's conjecture, so he wrote to his friend, the world-famous mathematician Leonhard Euler. Euler was unable to prove or disprove this conjecture, and it remains unsolved to this day. Write the numbers 16, 18, 20 as the sum of two primes.
A) 16 = 3 + 13, 18 = 1 + 17, 20 = 5 + 15
B) 16 = 13 + 3, 18 = 15 + 3, 20 = 16 + 4
C) 16 = 14 + 2, 18 = 13 + 5, 20 = 15 + 5
D) 16 = 13 + 3, 18 = 13 + 5, 20 = 13 + 7
E) 16 = 11 + 5, 18 = 11 + 7, 20 = 1 + 19

Question

In 1742 the mathematician Christian Goldbach observed that every even number (except 2) seemed representable as the sum of two primes. Goldbach could not prove this result, known today as Goldbach's conjecture, so he wrote to his friend, the world-famous mathematician Leonhard Euler. Euler was unable to prove or disprove this conjecture, and it remains unsolved to this day. Write the numbers 16, 18, 20 as the sum of two primes. ​
A) 16 = 3 + 13, 18 = 1 + 17, 20 = 5 + 15
B) 16 = 13 + 3, 18 = 15 + 3, 20 = 16 + 4
C) 16 = 14 + 2, 18 = 13 + 5, 20 = 15 + 5
D) 16 = 13 + 3, 18 = 13 + 5, 20 = 13 + 7
E) 16 = 11 + 5, 18 = 11 + 7, 20 = 1 + 19

Quizplus · Accepted Answer

- 16 = 13 + 3 (both 13 and 3 are prime)
- 18 = 13 + 5 (both 13 and 5 are prime)
- 20 = 13 + 7 (both 13 and 7 are prime)

Option (D) is the only one where all the pairs of primes add up to the given numbers (16, 18, 20). The other options either have non-prime numbers in their pairs or pairs that don't add up correctly.

In 1742 the Mathematician Christian Goldbach Observed That Every Even