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.
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.)
