Question Number 105170 by MJS last updated on 26/Jul/20

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are we able to decide the following
questions
(1) are there more or less primes with
p=n!−1 than with p=n!+1?
(2) are there n≠3 with n!−1 and n!+1
both are prime?
(3.1) are there n≠4, 5, 7 with √(n!+1)∈N?
(3.2) are there n>2 with √(n!−1)∈N?
(4.1) if ((n!+1)/(n+1))∈N∧n>1 ⇒ n=2k∧k∈N?
(4.2) is there an n>2 with ((n!−1)/(n−1))∈N?