Max N: <1,000,001
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Explanation:I was looking for a list of integers that satisfy Fermat's theorem:An odd prime N can be expressed as: N = v12 + v22 with v1 and v2 integers, if and only ifN = 1 + 4n (for some integer n). I did not find one, so I made a quick one myself.While I was at it, I used a special case of the Brahmagupta–Fibonacci identity (a2+b2)(c2+d2) = (ac-bd)2 + (ad+bc)2 = (ac+bd)2 + (ad-bc)2 to derive the Pythagorean primes. (You can make a right triangle with edges p1 and p2 and hypotinue N).Legend:
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