You noticed that it works for numbers below $100$, and others have already pointed out that it fails for $121 = 11\times 11$. Your algorithm relies on a simple observation : a number ($\geq2$) is prime if and only if it can be divided by another number than $1$ and itself.
The fact that you verified that your idea works for all numbers below $100$ (except for $1$, which isn't considered prime, but let's put that aside) proves that your algorithm is correct for the range $$. Your ideas are interesting for the problem of 'finding all prime numbers within a range'.
