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Erdős problem 1055

A prime pp is in class 11 if the only prime divisors of p+1p+1 are 22 or 33. In general, a prime pp is in class rr if every prime factor of p+1p+1 is in some class ≤r−1\leq r-1, with equality for at least one prime factor. Show that for each rr there exists a prime pp of class rr.

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