Find 2000 consecutive composite numbers.

(Of course you can't do this by trial and error alone)

For those who do not know what a composite number is, it is any integer greater than 1 that is not prime. (4, 6, 8, 9, ...)

Start with 2001! + 2 (that's 2 more than 2001 factorial, which latter is all the natural numbers through 2001 multiplied together). 2001! +2 is divisible by 2. 2001!+3 is divisible by 3. 2001!+4 is divisible by 4, ... , 2001!+2001 is divisible by 2001. This follows from 2001! itself being divisible by all these numbers; then adding an extra of each number gives another number also divisible by it.

Posted by Charlie on 2003-03-06 13:09:15