
theorem
  8839 is prime
proof
  now
    8839 = 2*4419 + 1; hence not 2 divides 8839 by NAT_4:9;
    8839 = 3*2946 + 1; hence not 3 divides 8839 by NAT_4:9;
    8839 = 5*1767 + 4; hence not 5 divides 8839 by NAT_4:9;
    8839 = 7*1262 + 5; hence not 7 divides 8839 by NAT_4:9;
    8839 = 11*803 + 6; hence not 11 divides 8839 by NAT_4:9;
    8839 = 13*679 + 12; hence not 13 divides 8839 by NAT_4:9;
    8839 = 17*519 + 16; hence not 17 divides 8839 by NAT_4:9;
    8839 = 19*465 + 4; hence not 19 divides 8839 by NAT_4:9;
    8839 = 23*384 + 7; hence not 23 divides 8839 by NAT_4:9;
    8839 = 29*304 + 23; hence not 29 divides 8839 by NAT_4:9;
    8839 = 31*285 + 4; hence not 31 divides 8839 by NAT_4:9;
    8839 = 37*238 + 33; hence not 37 divides 8839 by NAT_4:9;
    8839 = 41*215 + 24; hence not 41 divides 8839 by NAT_4:9;
    8839 = 43*205 + 24; hence not 43 divides 8839 by NAT_4:9;
    8839 = 47*188 + 3; hence not 47 divides 8839 by NAT_4:9;
    8839 = 53*166 + 41; hence not 53 divides 8839 by NAT_4:9;
    8839 = 59*149 + 48; hence not 59 divides 8839 by NAT_4:9;
    8839 = 61*144 + 55; hence not 61 divides 8839 by NAT_4:9;
    8839 = 67*131 + 62; hence not 67 divides 8839 by NAT_4:9;
    8839 = 71*124 + 35; hence not 71 divides 8839 by NAT_4:9;
    8839 = 73*121 + 6; hence not 73 divides 8839 by NAT_4:9;
    8839 = 79*111 + 70; hence not 79 divides 8839 by NAT_4:9;
    8839 = 83*106 + 41; hence not 83 divides 8839 by NAT_4:9;
    8839 = 89*99 + 28; hence not 89 divides 8839 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8839 & n is prime
  holds not n divides 8839 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
