Goldbach's Conjecture (1690)

In a 1742 letter to Euler, Christian Goldbach conjectured that every even integer greater than 2 is the sum of two primes: 4 = 2+2, 6 = 3+3, 8 = 3+5, 100 = 3+97, 1000 = 3+997. Verified computationally up to 4 × 10¹⁸ — four quintillion — the conjecture remains unproved after 282 years. It is the oldest unsolved problem in number theory. The closest result: Chen Jingrun proved in 1973 that every sufficiently large even number is the sum of a prime and a number with at most two prime factors.