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.)