998993

998993 is a notable number in the field of mathematics, particularly in the context of the Collatz conjecture. The Collatz conjecture, also known as the 3n + 1 problem, is an unsolved problem in mathematics that involves a sequence defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture states that this sequence will always reach 1, regardless of the starting value.

The number 998993 is significant because it is the smallest number for which the Collatz conjecture has not been proven or disproven. This means that while the conjecture has been verified for all numbers up to 998992, it remains an open question whether the sequence starting from 998993 will eventually reach 1. The study of this number and others like it is an active area of research in number theory and computational mathematics.