Goldbach Conjecture

An Early Statement

Every integer greater than 2 can be written as the sum of three primes.

$$\begin{array}{rl}3& =1+1+1,\\ 4& =1+1+2,\\ 5& =1+1+3=1+2+2,\\ 6& =1+2+3=2+2+2,\\ 7& =1+1+5=1+3+3=2+2+3.\end{array}$$

Note: 1 was considered prime back then.

Modern Statement

Every even integer greater than 2 is the sum of two primes.

$$\begin{array}{rl}4& =2+2,\\ 6& =3+3,\\ 8& =3+5,\\ 10& =3+7=5+5,\\ 12& =5+7.\end{array}$$

Statement in Section 14.1

Every even integer greater than 4 is the sum of two odd primes.

$$\begin{array}{rl}6& =3+3,\\ 8& =3+5,\\ 10& =3+7=5+5,\\ 12& =5+7.\end{array}$$