
theorem
  1373 is prime
proof
  now
    1373 = 2*686 + 1; hence not 2 divides 1373 by NAT_4:9;
    1373 = 3*457 + 2; hence not 3 divides 1373 by NAT_4:9;
    1373 = 5*274 + 3; hence not 5 divides 1373 by NAT_4:9;
    1373 = 7*196 + 1; hence not 7 divides 1373 by NAT_4:9;
    1373 = 11*124 + 9; hence not 11 divides 1373 by NAT_4:9;
    1373 = 13*105 + 8; hence not 13 divides 1373 by NAT_4:9;
    1373 = 17*80 + 13; hence not 17 divides 1373 by NAT_4:9;
    1373 = 19*72 + 5; hence not 19 divides 1373 by NAT_4:9;
    1373 = 23*59 + 16; hence not 23 divides 1373 by NAT_4:9;
    1373 = 29*47 + 10; hence not 29 divides 1373 by NAT_4:9;
    1373 = 31*44 + 9; hence not 31 divides 1373 by NAT_4:9;
    1373 = 37*37 + 4; hence not 37 divides 1373 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1373 & n is prime
  holds not n divides 1373 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
