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Panaitopol Primes

Published on Friday, 7th May 2010, 09:00 pm; Solved by 1212;
Difficulty rating: 45%

Problem 291

A prime number $p$ is called a Panaitopol prime if $p = \dfrac{x^4 - y^4}{x^3 + y^3}$ for some positive integers $x$ and $y$.

Find how many Panaitopol primes are less than 5×1015.