Prime Numbers

DIVISORS
A Divisor of a number is any integer that will evenly divide it.
the divisors of 1 are 1
the divisors of 5 are 1, 5
the divisors of 6 are 1, 2, 3, 6
the divisors of 7 are 1, 7
the divisors of 28 are 1, 2, 4, 7, 14, 28

PRIMES
Note that some numbers divisor list consists only of 1 and the number itself. These numbers are the Prime Numbers.
Examples are 2, 3, 5, 7, 11, 13, 17, 19, 23. By definition, 1 is not prime.

PROPER DIVISORS
The Proper Divisors of a number are the number's Divisors excluding the number itself. For the same examples shown above,
the proper divisors of 1 are
the proper divisors of 5 are 1
the proper divisors of 6 are 1, 2, 3
the proper divisors of 7 are 1
the proper divisors of 28 are 1, 2, 4, 7, 14
Notice that 1's proper divisor list is empty, because after excluding itself, there are no divisors left. Proper divisors are used to define the concept of perfect numbers. We can also define a Prime Number as an integer whose list of Proper Divisors consists only of the number 1. Since 1 fails to meet this criteria, it cannot be a Prime Number.

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