The details are quite complicated, but it works more or less like this. A public code - the code that everybody can see - is used to by multiplying two large prime numbers (of a few hundred digits each). The secret code is the factors involved. While it is easy to verify that the two factors - if somebody provides them - have the specified product, it is very hard to factor the large number and find the factors. No algorithm (method) is known that can do this factoring in a reasonable time.
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prime numbers only be used as encryption keys as in encryption the numbers are coded inj the form of 0s and 1s ,i.e binary form.
Data encryption, used for personal identification numbers (PINs) and for secure communications over the internet are based on very large prime numbers.
One interesting application of HUGE prime numbers is in encryption. Many systems used nowadays for encryption use more or less random prime numbers, of over a hundred digits each. This is by no means the only practical application of prime numbers. More examples of practical uses can be found here: http://en.wikipedia.org/wiki/Prime_number#Applications
I see no reason why they would do that. Prime numbers can be used for encryption, but there are algorithms that can quickly generate a more or less random prime number. No need to pay for the "discovery" of a specific number!
Data encryption, used for personal identification numbers (PINs) and for secure communications over the internet are based on very large prime numbers.