Collatz Conjecture Calculator
This Collatz conjecture calculator runs the famous 3n plus 1 process. Start with any whole number: if it is even, halve it; if it is odd, triple it and add one; then repeat. Enter a starting number up to a billion and the calculator counts how many steps it takes to reach 1 and records the highest value the sequence climbs to along the way. The Collatz conjecture says every starting number eventually reaches 1, and although it has been checked for enormous ranges, no one has ever proved it, which is what makes it one of the most famous unsolved problems in mathematics. The rule, a worked example and the assumptions are set out below.
The formula
Apply the map: if n is even, n becomes n/2; if n is odd, n becomes 3n + 1. Repeat until you reach 1. The number of applications is the total stopping time, and the conjecture is that this is always finite.
Worked example
Starting at 6: 6, 3, 10, 5, 16, 8, 4, 2, 1, which is 8 steps, peaking at 16. The number 27 famously takes 111 steps and peaks at 9232. Enter 27 to see it.
Frequently asked questions
What is the Collatz conjecture?
The claim that the 3n+1 process reaches 1 from every positive starting number. It is unproven but verified for very large ranges.
Why are these called hailstone numbers?
Because the values rise and fall repeatedly, like hailstones in a cloud, before finally settling to 1.
Does every number really reach 1?
It is conjectured to, and checked far beyond a billion, but there is no general proof.
Who this calculator is for
This calculator is for students, programmers and anyone exploring number theory.
What this calculator assumes
- You enter a whole number within the stated range.
- The exact integer algorithm is used.
- Very large results are shown grouped for readability.
Formula and sources
Related calculators
- Prime Factorization Calculator: break a number into prime factors.
- LCM Calculator: lowest common multiple.
- GCF Calculator: greatest common factor.
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