Collatz Conjecture

The Collatz conjecture, named after Lothar Collatz of Germany, proposed the conjecture in 1937. The conjecture states you must begin with any positive integer n: If it is an even number then halve it, or if it is an odd number then triple it and add 1. Do this recursively, and your result should always reach 1.

Please note: A maximum input length of 500 digits is enforced. Everything except positive numbers will be stripped out (including plus and minus signs) and must equal 1 or above. By entering ridiculously large numbers, the resulting page may be a few megabytes big.

Starting Integer: (required)

Main article: Collatz Conjecture - Information

It has long been undecided if the first step should or should not include the starting integer. Many documents state this uncertainty on the Internet. I'm following the OEIS examples A006577 and A008884. On my page, I shall use step 0 to show the starting integer.

Other names for the Collatz conjecture include the 3n+1 conjecture, the Ulam conjecture, Kakutani's problem, the Thwaites conjecture, Hasse's algorithm, and the Syracuse problem.

This tool was inspired by xkcd's comic #710 "Collatz Conjecture" from 05/03/2010.


I thought it might be interesting to some to include statistics about the data generated by use of this tool.

I've seen 1,428,051 unique starting integers. I have a total submission count of 1,512,219. The greatest number of steps I've seen from a submitted starting integer is 62,118 so far (abiding by the 500 digit length limitation) and was found on 18/01/2015. The most popular submitted starting integer has been submitted 20,396 times. The grand total number of steps produced by this tool is 318,641,716. This means a staggering grand total number of 6,649,326,097 digits were generated (including step #0 and the final result of 1), that equates to 6.19 GiBs of data.

These statistics began recording back in July, 2012.

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