1 and itself. It's a Prime number
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1001
The sum of 1,011 and 1,001 is 2,012. Unless they are binary numbers, in which case 1011 + 1001 = 10100
1000
All numbers except primes themselves can be written as a multiple of two or more primes. So you just need to try dividing the number by prime numbers. Trying 13 gives 1001 = 13*77 = 13*7*11. 13, 7 and 11 are all prime numbers, so you know you have found the unique prime factorization of 1001.
1001