Perfect numbers: numbers equal to the sum of their divisors
(excluding themselves)
6, 28, 496, 8128, ...
6 = 1 + 2 + 3
28 = 1 + 2 + 4 + 7 + 14 = 1 + 2 + 3 + 4 + 5 + 6 + 7
496 = 1 + 2 + 3 + 4 + ... + 31
8128 = 1 + 2 + 3 + 4 + ... + 127
28 = 13 + 33
496 = 13 + 33 + 53 + 73
8128 = 13 + 33 + 53 + 73 +
93 + 113 + 133 + 153
By the end of 1994, the largest Mersenne prime was 2 to the power of 859,433 minus 1.
In 2017 Church Deacon John Pace discovered the 50th Mersenne Prime by using GIMPS. The number 2 to the 77,232,917 minus 1 is more than 23 million digits long.
A year later, the 51st Mersenne Prime was discovered. It's 2 to the 82,589,933 minus 1, and this number has 24,862,048 digits.
As of today, this is still the largest known prime.