
theorem
  4243 is prime
proof
  now
    4243 = 2*2121 + 1; hence not 2 divides 4243 by NAT_4:9;
    4243 = 3*1414 + 1; hence not 3 divides 4243 by NAT_4:9;
    4243 = 5*848 + 3; hence not 5 divides 4243 by NAT_4:9;
    4243 = 7*606 + 1; hence not 7 divides 4243 by NAT_4:9;
    4243 = 11*385 + 8; hence not 11 divides 4243 by NAT_4:9;
    4243 = 13*326 + 5; hence not 13 divides 4243 by NAT_4:9;
    4243 = 17*249 + 10; hence not 17 divides 4243 by NAT_4:9;
    4243 = 19*223 + 6; hence not 19 divides 4243 by NAT_4:9;
    4243 = 23*184 + 11; hence not 23 divides 4243 by NAT_4:9;
    4243 = 29*146 + 9; hence not 29 divides 4243 by NAT_4:9;
    4243 = 31*136 + 27; hence not 31 divides 4243 by NAT_4:9;
    4243 = 37*114 + 25; hence not 37 divides 4243 by NAT_4:9;
    4243 = 41*103 + 20; hence not 41 divides 4243 by NAT_4:9;
    4243 = 43*98 + 29; hence not 43 divides 4243 by NAT_4:9;
    4243 = 47*90 + 13; hence not 47 divides 4243 by NAT_4:9;
    4243 = 53*80 + 3; hence not 53 divides 4243 by NAT_4:9;
    4243 = 59*71 + 54; hence not 59 divides 4243 by NAT_4:9;
    4243 = 61*69 + 34; hence not 61 divides 4243 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4243 & n is prime
  holds not n divides 4243 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
