# Prime number size and RSA decryption

Is there a former proof for why larger prime numbers make RSA securer? Maybe a theorem to show that it takes much more time to find out the private key if primes are larger?

Increasing the prime numbers does not necessarily lead to an increase in security of the RSA. As an example, when the private exponent is less than $$\frac{N^{\frac{1}{4}}}{3}$$, Wiener's attack is able to factor $$N$$ in the polynomial time.