  At present one can not find a single counterexample to even a simplest
version of Frobenius primality test. The assessment of probability of the
mistake, presented in [I.B. Damgard and G.S.Frandsen, Journal of Cryptology,
2006] is strongly overestimated. In the present paper, the properties of simple
divisors of FPP-numbers are proved. The lower bound for FPP are given.
