Question

The number of prime numbers among the numbers 105!+2,105!+3,105!+4, ... ,105!+105 is?!

Answer 1

A prime number is a number which is divisible only by 1 and the number itself.

There are no prime numbers here.

Every number in the set is divisible by the number added to the factorial, so it is not prime.

105!+2=2×3×4×...×105+2=
=2×(1+3×4×...×105)

It is an even number, so it is not prime.

105!+101=2×3×...×101×...×105+101=
(2×3×...100×102×103×104×105+1)×101

This number is divisinble by 101, so it is not prime.

All other numbers from this set can be expressed in this way, so they are not prime.