3x+1@home
3x+1@home is a distributed non-profit project trying to find high 3x+1 conjecture stopping times.
The 3x+1 conjecture is also known as Collatz conjecture, more information can be obtained here and here.
The collatz conjecture:
- Take any positive integer N.
- If its even, divide it by 2.
If its odd, multiply it with 3 and add 1. - Repeat step 2 until the number 1 is reached.
The Collatz conjecture is: For any positive integer the process above will reach the number one.
Some examples:
5 -> 16 -> 8 -> 4 -> 2 -> 1
Reached the number one in 5 steps. Stopping time is 5.
18 -> 9 -> 28 -> 14 -> 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
Reached the number one in 20 steps. Stopping time is 20.
More information about the Collatz conjecture can be found here
What is the stopping time (delay)?
The stopping time is equal to the number of steps needed to reach the number one.
What is 3x+1@home searching for?
3x+1@home is searching for high stopping times. Obviously huge integers have high stopping times, so what we are searching for is a high n=Stopping time / Log2(N). If N has an infinite stopping time, the application will also notice this.
A huge range of integers has already been checked by various projects, there is no need to check them again.
This project is checking the range between 271 and 272, a range that most likely hasn't been checked before.
Is 3x+1@home checking for strength, completeness, etc?
No. The application is optimized to calculate stopping times as fast as possible.