
theorem
  8849 is prime
proof
  now
    8849 = 2*4424 + 1; hence not 2 divides 8849 by NAT_4:9;
    8849 = 3*2949 + 2; hence not 3 divides 8849 by NAT_4:9;
    8849 = 5*1769 + 4; hence not 5 divides 8849 by NAT_4:9;
    8849 = 7*1264 + 1; hence not 7 divides 8849 by NAT_4:9;
    8849 = 11*804 + 5; hence not 11 divides 8849 by NAT_4:9;
    8849 = 13*680 + 9; hence not 13 divides 8849 by NAT_4:9;
    8849 = 17*520 + 9; hence not 17 divides 8849 by NAT_4:9;
    8849 = 19*465 + 14; hence not 19 divides 8849 by NAT_4:9;
    8849 = 23*384 + 17; hence not 23 divides 8849 by NAT_4:9;
    8849 = 29*305 + 4; hence not 29 divides 8849 by NAT_4:9;
    8849 = 31*285 + 14; hence not 31 divides 8849 by NAT_4:9;
    8849 = 37*239 + 6; hence not 37 divides 8849 by NAT_4:9;
    8849 = 41*215 + 34; hence not 41 divides 8849 by NAT_4:9;
    8849 = 43*205 + 34; hence not 43 divides 8849 by NAT_4:9;
    8849 = 47*188 + 13; hence not 47 divides 8849 by NAT_4:9;
    8849 = 53*166 + 51; hence not 53 divides 8849 by NAT_4:9;
    8849 = 59*149 + 58; hence not 59 divides 8849 by NAT_4:9;
    8849 = 61*145 + 4; hence not 61 divides 8849 by NAT_4:9;
    8849 = 67*132 + 5; hence not 67 divides 8849 by NAT_4:9;
    8849 = 71*124 + 45; hence not 71 divides 8849 by NAT_4:9;
    8849 = 73*121 + 16; hence not 73 divides 8849 by NAT_4:9;
    8849 = 79*112 + 1; hence not 79 divides 8849 by NAT_4:9;
    8849 = 83*106 + 51; hence not 83 divides 8849 by NAT_4:9;
    8849 = 89*99 + 38; hence not 89 divides 8849 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8849 & n is prime
  holds not n divides 8849 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
