Assuming that pn is the nth prime number, establish each of the following statements:(a) p...

Assuming that pn is the nth prime number, establish each of the following statements:

(a) pn > 2n − 1 for n ≥ 5.

(b) None of the integers Pn= p1p2⋯pn + 1 is a perfect square.

[Hint: Each Pn is of the form 4k + 3 for n > 1.]

(c) The sum

is never an integer.