### Largest Prime Number for 2016

As the new year approaches, you may be (or not be) interested to learn that the largest known prime number is 2^{74,207,281}– 1.

This number is an incredible 22 million digits long and 5 million digits longer than the second largest prime number. Hang on to your primes you might ask, “Why are prime numbers important? Are they of any practical use in real life?

What this means is that the time required to factorize integers into their **prime factors** grows (roughly) exponentially with the number of bits in the integer. So if the encryption uses very large integers, it would take an unrealistic amount of time to “crack” it.

If (or when) quantum computers become a reality, they would have the potential to make all of these algorithms obsolete, since there are quantum algorithms (in particular Shor’s algorithm) that can factor arbitrarily large integers much faster than any known classical algorithm. This has led to the very important field of post-quantum cryptography.”