
theorem
  3733 is prime
proof
  now
    3733 = 2*1866 + 1; hence not 2 divides 3733 by NAT_4:9;
    3733 = 3*1244 + 1; hence not 3 divides 3733 by NAT_4:9;
    3733 = 5*746 + 3; hence not 5 divides 3733 by NAT_4:9;
    3733 = 7*533 + 2; hence not 7 divides 3733 by NAT_4:9;
    3733 = 11*339 + 4; hence not 11 divides 3733 by NAT_4:9;
    3733 = 13*287 + 2; hence not 13 divides 3733 by NAT_4:9;
    3733 = 17*219 + 10; hence not 17 divides 3733 by NAT_4:9;
    3733 = 19*196 + 9; hence not 19 divides 3733 by NAT_4:9;
    3733 = 23*162 + 7; hence not 23 divides 3733 by NAT_4:9;
    3733 = 29*128 + 21; hence not 29 divides 3733 by NAT_4:9;
    3733 = 31*120 + 13; hence not 31 divides 3733 by NAT_4:9;
    3733 = 37*100 + 33; hence not 37 divides 3733 by NAT_4:9;
    3733 = 41*91 + 2; hence not 41 divides 3733 by NAT_4:9;
    3733 = 43*86 + 35; hence not 43 divides 3733 by NAT_4:9;
    3733 = 47*79 + 20; hence not 47 divides 3733 by NAT_4:9;
    3733 = 53*70 + 23; hence not 53 divides 3733 by NAT_4:9;
    3733 = 59*63 + 16; hence not 59 divides 3733 by NAT_4:9;
    3733 = 61*61 + 12; hence not 61 divides 3733 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3733 & n is prime
  holds not n divides 3733 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
