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Is there a prime number less than the product of consecutive primes, but greater than the last consecutive prime?
It's been a while since I graduated college, and I haven't used my degree since, but I started thinking about this problem this morning:
Consider a product of consecutive primes
$\Pi_{i=N}^{M}p_i = X$
Is there always a prime between $p_M$ and $X$?
I feel like there should be an elementary proof of this, but I haven't done any real math in almost 6 years now.