I have recently been reading about encryption and the importance of prime numbers and I have some questions that I would really appreciate some answers to, if possible:
- Is it correct that when creating encryption keys you take one large prime number, and then multiply it by another prime number to leave you with an even larger prime number?
- If 1 is correct, then is it correct to say "the reason for the large prime number calculation is it is very difficult and time consuming to work out what the initial prime numbers were used in the original calculation"?
- What constitutes as a large prime number?
The reason for this question is I have been doing some reading about encryption as stated above, and assuming the above statements are correct I think I have a really simple formula for working out what the original prime numbers used were. I have tested this prime numbers all the way up to $299993$. And I must be doing this wrong because it can not be this simple, I assume someone will point out where I am going wrong.