Erdos and Selfridge developed a scheme for classifying a prime number p: If the only factors of p+1 are 2 and 3, then put p in class 1. Otherwise, find the largest class r of the factors of p+1 and put p in class r+1.
For example, 11 is in class 1 because 12 has prime factors 2, 2, and 3. The number 43 is in class 2 because 44 has prime factors 2, 2, and 11, and all of those are in class 1. All Mersenne primes are in class 1, and all ugly numbers are in classes 1 or 2.
Write a function to classify prime numbers using this scheme.
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George Berken Augusto Mazzei Christian Schröder Mehdi Dehghan

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