Cody Problems 46054 and 46057 deal with the primorial p_n#, which is the product of all primes up to and including the nth prime p_n. The primorials corresponding to n = 1 through 5 are 2, 6, 30, 210, and 2310. Primorial primes are prime numbers that are either one smaller or one larger than a primorial. Examples include 3, 5, 7, 29, 31, 211, 2309, and 2311.
Write a function to identify primorial primes and their associated primorials. Given an input x, return a variable y with one of the following values:
y = 1 if x is a primorial prime
y = 0 if x is prime but not a primorial prime
y = -Inf if x is composite or 1
Also return a variable p that is the associated primorial in the first case and NaN in the other two cases.
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GeeTwo Tumo Quan Lorenzo

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