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On some properties of Fermat numbers. (English. Russian original) Zbl 1061.11500
Mosc. Univ. Math. Bull. 53, No. 5, 36-38 (1998); translation from Vestn. Mosk. Univ., Ser. I 1998, No. 5, 56-58 (1998).
Let \(\,F_m = 2^{2^m}+1\), \(\,m=0,1,2,\dots\,\) be the Fermat numbers. According to A. K. Lenstra, H. W. Lenstra, M. S. Manasse and J. M. Pollard [Math. Comput. 61, 319–349 (1993; Zbl 0792.11055)] the first five Fermat numbers are prime and \(F_5\) and all next \(F_m\) which were tested proved to be composite. The author sets out some tests to check whether the Fermat numbers are prime.

11A51 Factorization; primality
11Y11 Primality