some prime-related trick questions
 

Bored? Give these tests to your friends! :D

1. Some natural numbers have two factors. Some have three, some have four, and so on. How many have one factor?

2. Before 2[sup]6,972,593[/sup] - 1 was discovered, what was the largest Mersenne prime whose exponent was less than 10 million?

3. Find the factors of the prime number 2[sup]13,466,917[/sup] -1.

4. (This one's sorta dumb.) You want to do some math work with Prime95, MFAC (for double-Mersenne numbers), and Proth.exe (for Proth and other primes), but you only want one program to be running at once. Which do you load first?



















Answers:

1. All of them. Every natural number has at least one factor. Notice how I didn't use the word "exactly"?

2. 2[sup]6,972,593[/sup] - 1. It was always there, even before it is discovered.

3. 1 and 2[sup]13,466,917[/sup] - 1. Notice the word "prime".

4. Your computer.

G...r...o...a...n...!

On a more serious note, would this have been better to post in the solved puzzles section, because technically, the solution has already been given?