A German mathematician Christian Goldbach (1690-1764) stated that every odd composite number can be written as a sum of a prime and twice a square.

Some examples:
9 = 7 + 2*1²
21 = 3 + 2*3²
25 = 7 + 2*3²
33 = 31 +2*1²

Now we know that his conjecture is false.

What is the smallest odd composite number not complying with C.G.'s conjecture?

The two smallest odd composite numbers not complying with C.G's conjecture are 5777 and 5993.

Posted by K Sengupta on 2022-03-15 02:41:19