> log(p_n) < n (p_n^(1/n) - 1)

Let x = log(p_n)/n.

The the inequality asserts that

exp(x) > 1 + x

which is true for all positive real x

and hence for every prime p_n.

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> log(p_n) < n (p_n^(1/n) - 1)

Let x = log(p_n)/n.

The the inequality asserts that

exp(x) > 1 + x

which is true for all positive real x

and hence for every prime p_n.