Abstract
It is well known that 3, 5, 7 are such primes. But in higher regions they appear only very rare. There exist many residue classes without such primes. Also other conditions for their existence are given. Finally, 14 such primes less than 35 millions are listed.
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Aigner, A. Über Primzahlen, nach denen (fast) alle Fermatschen Zahlen quadratische Nichtreste sind. Monatshefte für Mathematik 101, 85–93 (1986). https://doi.org/10.1007/BF01298923
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DOI: https://doi.org/10.1007/BF01298923