Explore the famous 3n+1 Collatz conjecture. Enter any positive integer and see the complete sequence, total steps, peak value, and a visual chart. Free, instant, and runs entirely in your browser.
The Collatz conjecture (also known as the 3n+1 problem) is one of the most famous unsolved problems in mathematics. It states that no matter what positive integer you start with, the sequence will always eventually reach 1. Despite being simple to state, it has resisted proof for over 80 years. Our calculator lets you explore this fascinating sequence for any starting number.
The Collatz conjecture, proposed by Lothar Collatz in 1937, asks whether repeating two simple arithmetic operations — dividing even numbers by 2 and multiplying odd numbers by 3 and adding 1 — will eventually reach the number 1, regardless of the starting positive integer. Despite extensive computational verification for very large numbers, no general proof has been found.
The number with the most total stopping time found so far is around 2^68. The sequence for 27 is a famous example — it takes 111 steps and reaches a peak of 9,232 before finally reaching 1.
The Collatz conjecture is important because it demonstrates how a very simple rule can produce extremely complex and unpredictable behavior. It connects number theory, dynamical systems, and computational mathematics. Paul Erdős famously said "Mathematics may not be ready for such problems."
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