
theorem
  1973 is prime
proof
  now
    1973 = 2*986 + 1; hence not 2 divides 1973 by NAT_4:9;
    1973 = 3*657 + 2; hence not 3 divides 1973 by NAT_4:9;
    1973 = 5*394 + 3; hence not 5 divides 1973 by NAT_4:9;
    1973 = 7*281 + 6; hence not 7 divides 1973 by NAT_4:9;
    1973 = 11*179 + 4; hence not 11 divides 1973 by NAT_4:9;
    1973 = 13*151 + 10; hence not 13 divides 1973 by NAT_4:9;
    1973 = 17*116 + 1; hence not 17 divides 1973 by NAT_4:9;
    1973 = 19*103 + 16; hence not 19 divides 1973 by NAT_4:9;
    1973 = 23*85 + 18; hence not 23 divides 1973 by NAT_4:9;
    1973 = 29*68 + 1; hence not 29 divides 1973 by NAT_4:9;
    1973 = 31*63 + 20; hence not 31 divides 1973 by NAT_4:9;
    1973 = 37*53 + 12; hence not 37 divides 1973 by NAT_4:9;
    1973 = 41*48 + 5; hence not 41 divides 1973 by NAT_4:9;
    1973 = 43*45 + 38; hence not 43 divides 1973 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1973 & n is prime
  holds not n divides 1973 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
