Suppose, I know *m1, m2, m3* and *P1, P2, P3* of the following equations. Here *P1, P2, P3* are prime numbers.

*X mod P1 = m1*

*X mod P2 = m2*

*X mod P3 = m3*

Now, for another prime number *P4*,

I need to find, *X mod P4 = ?*

Using Chinese Remainder Theorem I can calculate this if *P4* is not a prime and is equal to *(P1xP2xP3)*.

How can I solve this problem for any prime *P4*?