
theorem
  859 is prime
proof
  now
    859 = 2*429 + 1; hence not 2 divides 859 by NAT_4:9;
    859 = 3*286 + 1; hence not 3 divides 859 by NAT_4:9;
    859 = 5*171 + 4; hence not 5 divides 859 by NAT_4:9;
    859 = 7*122 + 5; hence not 7 divides 859 by NAT_4:9;
    859 = 11*78 + 1; hence not 11 divides 859 by NAT_4:9;
    859 = 13*66 + 1; hence not 13 divides 859 by NAT_4:9;
    859 = 17*50 + 9; hence not 17 divides 859 by NAT_4:9;
    859 = 19*45 + 4; hence not 19 divides 859 by NAT_4:9;
    859 = 23*37 + 8; hence not 23 divides 859 by NAT_4:9;
    859 = 29*29 + 18; hence not 29 divides 859 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 859 & n is prime
  holds not n divides 859 by XPRIMET1:20;
  hence thesis by NAT_4:14;
