### Collatz Conjecture as a Computer Program

Collatz Conjecture as a Computer Program

One of the most famous unsolved mathematical conjectures totally lends itself to computer investigation.

It's the Collatz Conjecture, named after Lothar Collatz, who first proposed it in 1937. The great mathematician Stanisław Ulam not only failed to prove it but said, "perhaps mathematics is not ready for such problems".

Here it is as a computer program..

Pick any positive integer n
INFINITE LOOP
If n is even replace it by n/2
If n is odd replace it by 3*n+1
If n=1 bail out of loop
LOOP

The Collatz Conjecture says that no matter what number you start with you'll always bail out of the loop. In other words, no matter what number you start with you'll always reach 1.

The number of cycles needed to reach 1 is called the stopping time of n and denoted s(n). It turns out that the stopping time of a number is an interesting property and by no means simple.. for example s(27)=111

Mathematical statements phrased in terms of iteration seem to be especially nasty to prove. Perhaps Ulam was correct.. meaning mathematics was never designed for such problems!