In May 20 13, Harold Horovgott, a researcher at Paris Teachers College, published two papers, announcing that the weak Goldbach conjecture was completely proved.
It can be inferred from Goldbach's conjecture about even numbers that any odd number greater than 7 can be expressed as the sum of three odd prime numbers. The latter is called "weak Goldbach conjecture" or "Goldbach conjecture on odd numbers". If the Goldbach conjecture about even numbers is right, then the Goldbach conjecture about odd numbers will also be right.
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1742, Goldbach put forward the following conjecture in his letter to Euler: any integer greater than 2 can be written as the sum of three prime numbers. But Goldbach himself could not prove it, so he wrote to the famous mathematician Euler to help prove it, but until his death, Euler could not prove it.
Because the convention that "1 is also a prime number" is no longer used in mathematics, the modern statement of Goldbach conjecture is that any integer greater than 5 can be written as the sum of two prime numbers. (n>5: When n is even, n=2+(n-2) and n-2 is even, it can be decomposed into the sum of two prime numbers; When n is odd, n=3+(n-3), and n-3 is even, it can be decomposed into the sum of two prime numbers).
Euler also put forward another equivalent version in his defense, that is, any even number greater than 2 can be written as the sum of two prime numbers. The proposition "Any sufficiently large even number can be expressed as the sum of the number of prime factors not exceeding A and the number of other prime factors not exceeding B" is recorded as "a+b". 1966 Chen Jingrun proved that "1+2" holds, that is, "any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number".