
theorem
  857 is prime
proof
  now
    857 = 2*428 + 1; hence not 2 divides 857 by NAT_4:9;
    857 = 3*285 + 2; hence not 3 divides 857 by NAT_4:9;
    857 = 5*171 + 2; hence not 5 divides 857 by NAT_4:9;
    857 = 7*122 + 3; hence not 7 divides 857 by NAT_4:9;
    857 = 11*77 + 10; hence not 11 divides 857 by NAT_4:9;
    857 = 13*65 + 12; hence not 13 divides 857 by NAT_4:9;
    857 = 17*50 + 7; hence not 17 divides 857 by NAT_4:9;
    857 = 19*45 + 2; hence not 19 divides 857 by NAT_4:9;
    857 = 23*37 + 6; hence not 23 divides 857 by NAT_4:9;
    857 = 29*29 + 16; hence not 29 divides 857 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 857 & n is prime
  holds not n divides 857 by XPRIMET1:20;
  hence thesis by NAT_4:14;
end;
