
theorem
  1873 is prime
proof
  now
    1873 = 2*936 + 1; hence not 2 divides 1873 by NAT_4:9;
    1873 = 3*624 + 1; hence not 3 divides 1873 by NAT_4:9;
    1873 = 5*374 + 3; hence not 5 divides 1873 by NAT_4:9;
    1873 = 7*267 + 4; hence not 7 divides 1873 by NAT_4:9;
    1873 = 11*170 + 3; hence not 11 divides 1873 by NAT_4:9;
    1873 = 13*144 + 1; hence not 13 divides 1873 by NAT_4:9;
    1873 = 17*110 + 3; hence not 17 divides 1873 by NAT_4:9;
    1873 = 19*98 + 11; hence not 19 divides 1873 by NAT_4:9;
    1873 = 23*81 + 10; hence not 23 divides 1873 by NAT_4:9;
    1873 = 29*64 + 17; hence not 29 divides 1873 by NAT_4:9;
    1873 = 31*60 + 13; hence not 31 divides 1873 by NAT_4:9;
    1873 = 37*50 + 23; hence not 37 divides 1873 by NAT_4:9;
    1873 = 41*45 + 28; hence not 41 divides 1873 by NAT_4:9;
    1873 = 43*43 + 24; hence not 43 divides 1873 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1873 & n is prime
  holds not n divides 1873 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
