1. For any positive integer n, product of ‘n’ or
more than ‘n’ consecutive positive integers is divisible by n!.

For example, 63*64*65*.......*91 is divisible by 29!

2. If (n-1)! is not divisible by ‘n’, then n is a prime number. 4 is a special case here, which obeys this rule but not a prime.

3. From 1 & 2 above, we can conclude that, for any positive integer 'n-1', if the product of ‘n-1’ consecutive positive integers is not divisible by n, then n is a prime. But if divisible, we can't say that n is not a prime.

4. If a > b ≥ 3, then b

5. Product of two successive integers always ends in 2,6, or 0

6. The general perception about even numbers is even numbers start with 0 and go on 2,4,6,8,... and the odd numbers are 1,3,5,.... But negative integers are also to be categorized in to even and odd sets.

2. If (n-1)! is not divisible by ‘n’, then n is a prime number. 4 is a special case here, which obeys this rule but not a prime.

3. From 1 & 2 above, we can conclude that, for any positive integer 'n-1', if the product of ‘n-1’ consecutive positive integers is not divisible by n, then n is a prime. But if divisible, we can't say that n is not a prime.

4. If a > b ≥ 3, then b

^{a}> a^{b}where a,b Є Z+5. Product of two successive integers always ends in 2,6, or 0

6. The general perception about even numbers is even numbers start with 0 and go on 2,4,6,8,... and the odd numbers are 1,3,5,.... But negative integers are also to be categorized in to even and odd sets.

Hence the even number set is: ....-4,-2,0,2,4,6,.....

and the odd number set is: ....-5,-3,-1,3,5,7,.....

7. Why '1' is not a prime number?

A prime number can be defined

and the odd number set is: ....-5,-3,-1,3,5,7,.....

7. Why '1' is not a prime number?

A prime number can be defined

**as a positive integer that has exactly two different positive divisors, 1 and itself**. As the number '1' has only one positive divisor (ie., itself), it is not a prime number.
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