【Question 5】
In the eighteenth century, mathematician Goldbach discovered while studying natural numbers that many even numbers share a common property, which can be expressed as the sum of two odd prime numbers. Thus, he proposed a conjecture: Can any even number greater than 2 be expressed as the sum of two odd prime numbers?
【Analysis and Solution】
On June 7, 1742, Prussian mathematician Christian Goldbach, in a letter to Swiss mathematician Leonhard Euler, proposed the following conjecture: "Any integer greater than 2 can be written as the sum of three prime numbers." This statement differs from the current one because Goldbach adhered to the convention that "1 is also a prime number." The modern mathematical community no longer uses this convention. The modern statement of Goldbach's original conjecture is: "Any integer greater than 5 can be written as the sum of three prime numbers." In his reply on June 30, Euler noted that this conjecture can have another equivalent version: "Any even number greater than 2 can be written as the sum of two prime numbers." He regarded this conjecture as a theorem but was unable to prove it. The commonly seen statement of the conjecture today is Euler's version, also known as the "Strong Goldbach Conjecture" or the "Goldbach Conjecture for even numbers." From the Goldbach Conjecture for even numbers, it can be deduced that: "Any odd number greater than 5 can be written as the sum of three prime numbers." This is known as the "Weak Goldbach Conjecture" or the "Goldbach Conjecture for odd numbers." If the Goldbach Conjecture for even numbers is true, then the Goldbach Conjecture for odd numbers is also true.
4 can only be expressed as $4=1+3=2+2$, meaning 4 cannot be expressed as the sum of two odd prime numbers. Therefore, the answer is “×”.