129-digit number
114,381,625,757,888,867,669,235,779,
976,146,612,010,218,296,721,242,362,
562,561,842,935,706,935,245,733,
897,830,597,123,563,958,705,058,
989,075,147,599,290,026,879,543,541
This number is better-known as RSA-129.
It was posted in a 1977 magazine article as a challenge.
The co-inventors of RSA Cryptography wanted to see just how hard it was to factorize a number (it was crucial to the new technology).
RSA-129 is created by multiplying two very large prime numbers.
Ron Rivest (the R in RSA) thought it would take 40 quadrillion years for the prime numbers to be found.
He was wrong. It took 17 years.
I also recommend the extra footage at Numberphile2, which is some extra questions I asked Professor Rivest.