Elementary Proof of the Existence of at Least p_n − 2 Primes Between p_n and the Primorial p_n#

<p dir="ltr">This work presents an elementary and rigorous proof that there are at least pn−2 prime numbers in the interval between the prime pn and its primorial pn#, defined as the product of the first n prime numbers. The proof relies on accessible arithmetic arguments, avoiding advanced analytical tools, and is intended to be understandable even to readers with a basic background in number theory.</p>