
theorem
  6199 is prime
proof
  now
    6199 = 2*3099 + 1; hence not 2 divides 6199 by NAT_4:9;
    6199 = 3*2066 + 1; hence not 3 divides 6199 by NAT_4:9;
    6199 = 5*1239 + 4; hence not 5 divides 6199 by NAT_4:9;
    6199 = 7*885 + 4; hence not 7 divides 6199 by NAT_4:9;
    6199 = 11*563 + 6; hence not 11 divides 6199 by NAT_4:9;
    6199 = 13*476 + 11; hence not 13 divides 6199 by NAT_4:9;
    6199 = 17*364 + 11; hence not 17 divides 6199 by NAT_4:9;
    6199 = 19*326 + 5; hence not 19 divides 6199 by NAT_4:9;
    6199 = 23*269 + 12; hence not 23 divides 6199 by NAT_4:9;
    6199 = 29*213 + 22; hence not 29 divides 6199 by NAT_4:9;
    6199 = 31*199 + 30; hence not 31 divides 6199 by NAT_4:9;
    6199 = 37*167 + 20; hence not 37 divides 6199 by NAT_4:9;
    6199 = 41*151 + 8; hence not 41 divides 6199 by NAT_4:9;
    6199 = 43*144 + 7; hence not 43 divides 6199 by NAT_4:9;
    6199 = 47*131 + 42; hence not 47 divides 6199 by NAT_4:9;
    6199 = 53*116 + 51; hence not 53 divides 6199 by NAT_4:9;
    6199 = 59*105 + 4; hence not 59 divides 6199 by NAT_4:9;
    6199 = 61*101 + 38; hence not 61 divides 6199 by NAT_4:9;
    6199 = 67*92 + 35; hence not 67 divides 6199 by NAT_4:9;
    6199 = 71*87 + 22; hence not 71 divides 6199 by NAT_4:9;
    6199 = 73*84 + 67; hence not 73 divides 6199 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6199 & n is prime
  holds not n divides 6199 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
