
theorem
  6737 is prime
proof
  now
    6737 = 2*3368 + 1; hence not 2 divides 6737 by NAT_4:9;
    6737 = 3*2245 + 2; hence not 3 divides 6737 by NAT_4:9;
    6737 = 5*1347 + 2; hence not 5 divides 6737 by NAT_4:9;
    6737 = 7*962 + 3; hence not 7 divides 6737 by NAT_4:9;
    6737 = 11*612 + 5; hence not 11 divides 6737 by NAT_4:9;
    6737 = 13*518 + 3; hence not 13 divides 6737 by NAT_4:9;
    6737 = 17*396 + 5; hence not 17 divides 6737 by NAT_4:9;
    6737 = 19*354 + 11; hence not 19 divides 6737 by NAT_4:9;
    6737 = 23*292 + 21; hence not 23 divides 6737 by NAT_4:9;
    6737 = 29*232 + 9; hence not 29 divides 6737 by NAT_4:9;
    6737 = 31*217 + 10; hence not 31 divides 6737 by NAT_4:9;
    6737 = 37*182 + 3; hence not 37 divides 6737 by NAT_4:9;
    6737 = 41*164 + 13; hence not 41 divides 6737 by NAT_4:9;
    6737 = 43*156 + 29; hence not 43 divides 6737 by NAT_4:9;
    6737 = 47*143 + 16; hence not 47 divides 6737 by NAT_4:9;
    6737 = 53*127 + 6; hence not 53 divides 6737 by NAT_4:9;
    6737 = 59*114 + 11; hence not 59 divides 6737 by NAT_4:9;
    6737 = 61*110 + 27; hence not 61 divides 6737 by NAT_4:9;
    6737 = 67*100 + 37; hence not 67 divides 6737 by NAT_4:9;
    6737 = 71*94 + 63; hence not 71 divides 6737 by NAT_4:9;
    6737 = 73*92 + 21; hence not 73 divides 6737 by NAT_4:9;
    6737 = 79*85 + 22; hence not 79 divides 6737 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6737 & n is prime
  holds not n divides 6737 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
