From The Daily Dot:
To date, there is no known shortcut to quickly factor large integers into primes. It has never been proven that no such shortcut exists. We’ve just never found one.
If the unfactorable nature of these large integers doesn’t interest you, consider that it has been the reason many of your most personal messages are kept private as they move across the Internet.
But the Times report about how the NSA penetrated banking encryption seems to suggest the agency may have cracked the problem. Here’s why (and this is going to take some explaining):
They go on to explain how primes, public key encryption, and the RSA algorithm are related. Nicely done. Great read.