
theorem
  887 is prime
proof
  now
    887 = 2*443 + 1; hence not 2 divides 887 by NAT_4:9;
    887 = 3*295 + 2; hence not 3 divides 887 by NAT_4:9;
    887 = 5*177 + 2; hence not 5 divides 887 by NAT_4:9;
    887 = 7*126 + 5; hence not 7 divides 887 by NAT_4:9;
    887 = 11*80 + 7; hence not 11 divides 887 by NAT_4:9;
    887 = 13*68 + 3; hence not 13 divides 887 by NAT_4:9;
    887 = 17*52 + 3; hence not 17 divides 887 by NAT_4:9;
    887 = 19*46 + 13; hence not 19 divides 887 by NAT_4:9;
    887 = 23*38 + 13; hence not 23 divides 887 by NAT_4:9;
    887 = 29*30 + 17; hence not 29 divides 887 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 887 & n is prime
  holds not n divides 887 by XPRIMET1:20;
  hence thesis by NAT_4:14;
end;
