Is 269 a prime number or a composite number? What is the calculation idea? We already know that it's a prime number. We need to calculate the main idea

Is 269 a prime number or a composite number? What is the calculation idea? We already know that it's a prime number. We need to calculate the main idea

It's obviously prime
Sum: the common divisor has other numbers besides 1 and itself
1. Suppose: if it is a composite number, it must be decomposed into two numbers a × B (where a and B are not 1 or 269). This sentence can also be equivalent to the existence of at least one pair of above conditions a and B such that a × B = 269, that is, we can prove that it is a composite number as long as we find a pair of such numbers
2. Conjecture of a and B: no matter how much a and B are, the bits of the number obtained by multiplying the numbers on its two bits must be nine. But in the multiplication formula, only 1 × 9 = 9; 3 × 3 = 9; 7 × 7 = 49
3. Take a number of 1 and 9 and say: 1 is definitely not good, if a = 11, B is a fraction, not good. Similarly, 21, 31, 41, 51, 61, 71, 81, 91 are not good. You can see that you don't need to count more than 100!
Let's take two numbers with a bit of 3 and say: using the above method, 3, 13, 23, 33 and 93 are not good. Case 2 fails!
Finally, take a number of 7 to say: 7, 17, 97 are not, no need to prove
So 269 must be prime