How do people find big primes? These primes have millions of digits, and may take years of collective effort and computing power to be found. Unsurprisingly, mathematicians have figured out various ways to more efficiently and accurately find these big primes. In the process, the unique and interesting properties of various primes have also been found.
Great Internet Mersenne Prime Search:
https://www.mersenne.org/
PrimeGrid
https://www.primegrid.com/
Other resources
PrimePages - collection of all the largest primes : https://primes.utm.edu/primes/
Primality Proving - the math behind prime proofs: https://primes.utm.edu/prove/index.html
Wolfram MathWorld article on Mersenne primes: https://mathworld.wolfram.com/MersennePrime.html
Images
https://species.wikimedia.org/wiki/Magicicada
https://commons.wikimedia.org/wiki/File:Godfrey_Harold_Hardy_1.jpg
https://esahubble.org/images/heic2112a/
https://esahubble.org/images/potw1411a/
https://hubblesite.org/contents/media/images/2021/007/01FFN7MSBMTA4GPPNQZ0Y6CX8Z?
Music
https://c418.bandcamp.com/album/mixes
No but Yes by C418
https://c418.bandcamp.com/album/dief
Blank Cubical by C418
Match Cut by C418
Work Life Imbalance by C418