It's the simplest open problem in mathematics, so simple a child can understand it:
Pick a whole number bigger than zero. If it's odd, multiply by three and add one. If it's even, divide by two. Take the result and repeat the procedure. Do all numbers eventually reach 1 and the cycle 4, 2, 1?
In 1937, Lothar Collatz conjectured that, yes, every whole number bigger than zero cycles at 4, 2, 1. But, to this day, the proof of this conjecture has eluded the best mathematicians. Eminent mathematician Paul Erdős said, "Mathematics may not be ready for such problems." Perhaps that is true. Or, perhaps you, dear reader, can prove or disprove Collatz's conjecture. Only time will tell.
For now, experimental mathematicians have verified the conjecture for every number up to 260. That's a ridiculously large number, but not a proof. There may yet be some ginormous number that disproves the conjecture. (Such a thing has happened before, like with the Mertens conjecture.) That's where this repository comes in.
Experimental mathematicians need software to probe the sequence. Maple and Mathematica are good choices, considered by some sine non qua for work of this kind, but I prefer optimized algorithms. Here in you'll find:
- Software to explore hailstone sequences
- Results of prior calculations
- Reference materials and links
Happy hunting! But remember this warning:
