All Elite Primes Up to 250 Billion
نویسندگان
چکیده
A prime number p is called elite if only finitely many Fermat numbers 2 n + 1 are quadratic residues of p. Previously only the interval up to 10 was systematically searched for elite primes and 16 such primes were found. We extended this research up to 2.5 · 10 and found five further elites, among which 1 151 139 841 is the smallest and 171 727 482 881 the largest.
منابع مشابه
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An odd prime number p is called anti-elite if only finitely many Fermat numbers are quadratic non-residues to p. This concept is the exact opposite to that of elite prime numbers. We study some fundamental properties of anti-elites and show that there are infinitely many of them. A computational search among all the numbers up to 100 billion yielded 84 anti-elite primes.
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