A new proof for a conjecture on geometric mean of primes

There is a conjecture on primes that states that if denote the nth prime, then, where,and also we knowis the geometric mean of the first n primes. This conjecture in the first time proved by Sndor and Verroken, see [4], and revisited by Hassani in 2013, see [2]. Now, in this work we want to prove this conjecture by the simpler way