We consider the Frobenius problem for the 3-dim numerical semigroup S(d 1 , d 2 , d 3 ) generated by three positive integers d 1 , d 2 , d 3 with gcd(d 1 , d 2 , d 3 ) = 1 and calculate weak (Cesaro) asymptotics of its conductor C(d 1 , d 2 , d 3 ) and the fraction p(d 1 , d 2 , d 3 ) of the segment [0; C(d 1 , d 2 , d 3 ) − 1] occupied by the semigroup. Four conjectures # 1999-8, # 1999-9, # 1999-10 and # 2003-5 which were posed by V.I. Arnold (Arnold's Problems, pp. 129-130, 163, 2004) and devoted to the statistics of the m-dim semigroups, m ≥ 3, are refuted for the case m = 3.