
theorem
  953 is prime
proof
  now
    953 = 2*476 + 1; hence not 2 divides 953 by NAT_4:9;
    953 = 3*317 + 2; hence not 3 divides 953 by NAT_4:9;
    953 = 5*190 + 3; hence not 5 divides 953 by NAT_4:9;
    953 = 7*136 + 1; hence not 7 divides 953 by NAT_4:9;
    953 = 11*86 + 7; hence not 11 divides 953 by NAT_4:9;
    953 = 13*73 + 4; hence not 13 divides 953 by NAT_4:9;
    953 = 17*56 + 1; hence not 17 divides 953 by NAT_4:9;
    953 = 19*50 + 3; hence not 19 divides 953 by NAT_4:9;
    953 = 23*41 + 10; hence not 23 divides 953 by NAT_4:9;
    953 = 29*32 + 25; hence not 29 divides 953 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 953 & n is prime
  holds not n divides 953 by XPRIMET1:20;
  hence thesis by NAT_4:14;
end;
