1. Mersenne numbers (of the form 2^n - 1) are far easier to prove primality than other similarly sized numbers. It looks like there is a registry! Details for

1. Mersenne numbers (of the form 2^n - 1) are far easier to prove primality than other similarly sized numbers. It looks like there is a registry! Details for adding an item are at https://primes.utm.edu/notes/faq/add_prime.html https://primes.utm.edu/notes/faq/add_prime.html 2. We haven't enumerated the vast majority of the primes under this. There could even be mersenne primes as yet unexamined smaller than this, as the search is distributed. And whenever an ssl certificate is generated, two (hopefully) previously undiscovered prime numbers is found. (For 1024-bit length keys, that's around 308 digits.) The magnitude of the numbers involved is hard to think about. The number of protons in the observable universe "only" has around 80 digits. References: * Mersenne primes - https://en.wikipedia.org/wiki/Mersenne_prime https://en.wikipedia.org/wiki/Mersenne_prime * Eddington number -https://en.wikipedia.org/wiki/Eddington_number https://en.wikipedia.org/wiki/Eddington_number