Composed of 10 distinct prime factors. Has 2048 divisors. Prime factorization: 3³ × 7 × 11 × 13 × 37 × 73 × 101 × 137 × 9901 × 99990001. Abundance is 106848627528278203924482
Prime numbers are natural numbers greater than 1 that cannot be divided by smaller numbers. Prime factorization decomposes composite numbers into prime factors. Fundamental theorem states that all natural numbers greater than 1 are prime or factorizable
Partition of n is writing n as sum of positive integers. Two sums differing only in order are considered same partition. Partitions can be visualized using Ferrers or Young diagrams. Number of partitions of n is given by partition function p(n)
A square number is an integer that is the square of itself. Square numbers are non-negative integers. The nth square number is n², with 0² being the zeroth. Square numbers can be represented by arranging points in a square
The Collatz conjecture asks if positive integers eventually converge to 1. Even numbers are divided by 2, odd numbers are multiplied by 3 and added 1. The sequence is called the hailstone sequence or wondrous numbers
Googolplex is defined as 10^10^100 or one followed by 10^100 zeroes. Milton Sirotta originally defined it as "one, then writing zeroes until tired". Edward Kasner redefined it to its current value