# In RSA, must $p$ and $q$ have the same number of bits?

Is it necessary to take the same bit size of "p" and "q" in case of RSA algorithm? i had read that bitsize of p and q must be same. BUT after calculating, i found that bit size could be different also. But time complexity will increase. Can anyone help me?

The RSA method works regardless of the size of the individual primes $p,q$. The reason that we would want $p$ and $q$ to be of roughly equal size is that one method of breaking RSA is factoring $n = pq$, and the running time of some factoring methods (notably ECM, the elliptic curve method) depends on the size of the smallest prime factor of $n$. Therefore to get the most "bang for the buck", you would like $p,q$ to be both as large as possible under the constraint on the size of $n$ (which determines the speed of encryption and decryption), and so of roughly equal size.
Since, anyone knows n = pq, prime factor of n can be found to calculate its private key. If your q is too small say 19, and p is very large say 1000 bits prime number, you can easily get p from n just dividing it by a small number. So, both number p and q must be sufficiently large. They cannot be exact of same size but almost equal in size. Size is too large.