It is a crime to even be in possession of some numbers in United States. In the following video, Sam from Wendover Productions explains this seemingly strange state of affairs:
If you'd like to try your hand at identifying other prime numbers that might someday also be made illegal to possess in America, join the Great Internet Mersenne Prime Search, which just confirmed the 45th Mersenne prime number to be discovered back on 2 September 2016 after 8 years of computer-aided labor!
As for the biggest prime number known today, which is the 49th Mersenne prime, it was confirmed as such on 7 January 2016:
Of course, for non-mathematicians, no prime number really exists until it's printed out on paper.
Just be sure that it's not one of the ones that you don't want the cops to catch you with!