
theorem
  8237 is prime
proof
  now
    8237 = 2*4118 + 1; hence not 2 divides 8237 by NAT_4:9;
    8237 = 3*2745 + 2; hence not 3 divides 8237 by NAT_4:9;
    8237 = 5*1647 + 2; hence not 5 divides 8237 by NAT_4:9;
    8237 = 7*1176 + 5; hence not 7 divides 8237 by NAT_4:9;
    8237 = 11*748 + 9; hence not 11 divides 8237 by NAT_4:9;
    8237 = 13*633 + 8; hence not 13 divides 8237 by NAT_4:9;
    8237 = 17*484 + 9; hence not 17 divides 8237 by NAT_4:9;
    8237 = 19*433 + 10; hence not 19 divides 8237 by NAT_4:9;
    8237 = 23*358 + 3; hence not 23 divides 8237 by NAT_4:9;
    8237 = 29*284 + 1; hence not 29 divides 8237 by NAT_4:9;
    8237 = 31*265 + 22; hence not 31 divides 8237 by NAT_4:9;
    8237 = 37*222 + 23; hence not 37 divides 8237 by NAT_4:9;
    8237 = 41*200 + 37; hence not 41 divides 8237 by NAT_4:9;
    8237 = 43*191 + 24; hence not 43 divides 8237 by NAT_4:9;
    8237 = 47*175 + 12; hence not 47 divides 8237 by NAT_4:9;
    8237 = 53*155 + 22; hence not 53 divides 8237 by NAT_4:9;
    8237 = 59*139 + 36; hence not 59 divides 8237 by NAT_4:9;
    8237 = 61*135 + 2; hence not 61 divides 8237 by NAT_4:9;
    8237 = 67*122 + 63; hence not 67 divides 8237 by NAT_4:9;
    8237 = 71*116 + 1; hence not 71 divides 8237 by NAT_4:9;
    8237 = 73*112 + 61; hence not 73 divides 8237 by NAT_4:9;
    8237 = 79*104 + 21; hence not 79 divides 8237 by NAT_4:9;
    8237 = 83*99 + 20; hence not 83 divides 8237 by NAT_4:9;
    8237 = 89*92 + 49; hence not 89 divides 8237 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8237 & n is prime
  holds not n divides 8237 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
