
theorem
  8837 is prime
proof
  now
    8837 = 2*4418 + 1; hence not 2 divides 8837 by NAT_4:9;
    8837 = 3*2945 + 2; hence not 3 divides 8837 by NAT_4:9;
    8837 = 5*1767 + 2; hence not 5 divides 8837 by NAT_4:9;
    8837 = 7*1262 + 3; hence not 7 divides 8837 by NAT_4:9;
    8837 = 11*803 + 4; hence not 11 divides 8837 by NAT_4:9;
    8837 = 13*679 + 10; hence not 13 divides 8837 by NAT_4:9;
    8837 = 17*519 + 14; hence not 17 divides 8837 by NAT_4:9;
    8837 = 19*465 + 2; hence not 19 divides 8837 by NAT_4:9;
    8837 = 23*384 + 5; hence not 23 divides 8837 by NAT_4:9;
    8837 = 29*304 + 21; hence not 29 divides 8837 by NAT_4:9;
    8837 = 31*285 + 2; hence not 31 divides 8837 by NAT_4:9;
    8837 = 37*238 + 31; hence not 37 divides 8837 by NAT_4:9;
    8837 = 41*215 + 22; hence not 41 divides 8837 by NAT_4:9;
    8837 = 43*205 + 22; hence not 43 divides 8837 by NAT_4:9;
    8837 = 47*188 + 1; hence not 47 divides 8837 by NAT_4:9;
    8837 = 53*166 + 39; hence not 53 divides 8837 by NAT_4:9;
    8837 = 59*149 + 46; hence not 59 divides 8837 by NAT_4:9;
    8837 = 61*144 + 53; hence not 61 divides 8837 by NAT_4:9;
    8837 = 67*131 + 60; hence not 67 divides 8837 by NAT_4:9;
    8837 = 71*124 + 33; hence not 71 divides 8837 by NAT_4:9;
    8837 = 73*121 + 4; hence not 73 divides 8837 by NAT_4:9;
    8837 = 79*111 + 68; hence not 79 divides 8837 by NAT_4:9;
    8837 = 83*106 + 39; hence not 83 divides 8837 by NAT_4:9;
    8837 = 89*99 + 26; hence not 89 divides 8837 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8837 & n is prime
  holds not n divides 8837 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
