MATH QUESTION! please help! College math course.?

Question

1. Name a factor of 31!+29---The number 29 more than 31!

2. find 5000 consecutive numbers that are composite. HINT- A good first try is to consider the numbers starting with 5000!+2

3. Prove that every prime p>3 is either one more or one less than a number divisible by 6.

Answer 1

1.) 31! is divisible by 29, so 31! + 29 is also divisible by 29.

2.) 5000! + 2 is divisible by 2.
5000! + 3 is divisible by 3.
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5000! +5000 is divisible by 5000.
5000! + 5001 is divisible by 3.
That's 5000 consecutive composite numbers.

3.) A number 2 more than a multiple of 6 is divisible by 2.
A number 3 more than a multiple of 6 is divisible by 3.
A number 4 more than a multiple of 6 is divisible by 2.