[jdewerd]

The 50 000 000th prime is 982451653, but fun fact: you may have already memorized a prime much larger than this without even realizing you have done so!

2^255-19

This is where Curve 25519 and the associated cryptography (ed25519, x25519) gets its name from. Written out, 2^255-19=57896044618658097711785492504343953926634992332820282019728792003956564819949.

[lifthrasiir]

You could have memorized even large one if you are familiar with the full name of the Mersenne Twister PRNG: MT19937 is named so because its period is 2^19937-1 which is a prime number (in fact, the largest known one at the time of Zigler's writing). In my knowledge any larger prime number hasn't been used for the practical purpose.

[jdewerd]

Cool, I hadn't run into it before so thanks for introducing me!

I was going to include the digits for comparison, but yes, on second thought 6002 digits is probably too much for polite inclusion in a HN post.

[shric]

Yeah, although that's better than 19937 ones in a row.

[quuxplusone]

https://oeis.org/A004023 "Indices of prime repunits: numbers k such that 11...111 (with k 1's) = (10^k - 1)/9 is prime."

OEIS says "19937 ones in a row" isn't prime, but "1031 ones in a row" is.

And "8177207 ones in a row" is at least a probable prime. (Which you can maybe remember as a seven-digit phone number, or as either BITTZOT or LOZLLIB depending on how you prefer to hold your calculator. But those mnemonics are wasted if (10^{81777207}-1)/9 turns out to be merely pseudoprime.)

[ape4]

On a Linux command line:

    echo '2^255-19' | bc