
theorem
  4373 is prime
proof
  now
    4373 = 2*2186 + 1; hence not 2 divides 4373 by NAT_4:9;
    4373 = 3*1457 + 2; hence not 3 divides 4373 by NAT_4:9;
    4373 = 5*874 + 3; hence not 5 divides 4373 by NAT_4:9;
    4373 = 7*624 + 5; hence not 7 divides 4373 by NAT_4:9;
    4373 = 11*397 + 6; hence not 11 divides 4373 by NAT_4:9;
    4373 = 13*336 + 5; hence not 13 divides 4373 by NAT_4:9;
    4373 = 17*257 + 4; hence not 17 divides 4373 by NAT_4:9;
    4373 = 19*230 + 3; hence not 19 divides 4373 by NAT_4:9;
    4373 = 23*190 + 3; hence not 23 divides 4373 by NAT_4:9;
    4373 = 29*150 + 23; hence not 29 divides 4373 by NAT_4:9;
    4373 = 31*141 + 2; hence not 31 divides 4373 by NAT_4:9;
    4373 = 37*118 + 7; hence not 37 divides 4373 by NAT_4:9;
    4373 = 41*106 + 27; hence not 41 divides 4373 by NAT_4:9;
    4373 = 43*101 + 30; hence not 43 divides 4373 by NAT_4:9;
    4373 = 47*93 + 2; hence not 47 divides 4373 by NAT_4:9;
    4373 = 53*82 + 27; hence not 53 divides 4373 by NAT_4:9;
    4373 = 59*74 + 7; hence not 59 divides 4373 by NAT_4:9;
    4373 = 61*71 + 42; hence not 61 divides 4373 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4373 & n is prime
  holds not n divides 4373 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
