Let N = 111 ... 1222 ... 2, i.e. 1999 digits of digit 1 followed by 1999 digits of 2.
Express N as a product of four integers, none of them equal to 1.
111222 = 2*3*167*111
11112222 = 2*3*1667*1111
1111122222 = 2*3*16667*11111
If there are 1999 1's and 1999 2's, then four numbers which multiply to this are:
2
3
1...1997 6's...7
1999 1's
Only the 2 and the 3 are guaranteed to be prime.

Posted by Charlie
on 20151106 09:56:37 