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is divisible by all numbers up to and including 5. This includes primes 2, 3 and 5. Now, if that's true, then 5! + 1 is not divisible by any of those numbers. 1 is not prime. and 5! is not divisible by 2 since 5! (or in the question 100!) is even and 5! + 1 is odd.
so for 100! + 1, the least prime has to be greater than not only 40 but also 100.