
theorem
  6197 is prime
proof
  now
    6197 = 2*3098 + 1; hence not 2 divides 6197 by NAT_4:9;
    6197 = 3*2065 + 2; hence not 3 divides 6197 by NAT_4:9;
    6197 = 5*1239 + 2; hence not 5 divides 6197 by NAT_4:9;
    6197 = 7*885 + 2; hence not 7 divides 6197 by NAT_4:9;
    6197 = 11*563 + 4; hence not 11 divides 6197 by NAT_4:9;
    6197 = 13*476 + 9; hence not 13 divides 6197 by NAT_4:9;
    6197 = 17*364 + 9; hence not 17 divides 6197 by NAT_4:9;
    6197 = 19*326 + 3; hence not 19 divides 6197 by NAT_4:9;
    6197 = 23*269 + 10; hence not 23 divides 6197 by NAT_4:9;
    6197 = 29*213 + 20; hence not 29 divides 6197 by NAT_4:9;
    6197 = 31*199 + 28; hence not 31 divides 6197 by NAT_4:9;
    6197 = 37*167 + 18; hence not 37 divides 6197 by NAT_4:9;
    6197 = 41*151 + 6; hence not 41 divides 6197 by NAT_4:9;
    6197 = 43*144 + 5; hence not 43 divides 6197 by NAT_4:9;
    6197 = 47*131 + 40; hence not 47 divides 6197 by NAT_4:9;
    6197 = 53*116 + 49; hence not 53 divides 6197 by NAT_4:9;
    6197 = 59*105 + 2; hence not 59 divides 6197 by NAT_4:9;
    6197 = 61*101 + 36; hence not 61 divides 6197 by NAT_4:9;
    6197 = 67*92 + 33; hence not 67 divides 6197 by NAT_4:9;
    6197 = 71*87 + 20; hence not 71 divides 6197 by NAT_4:9;
    6197 = 73*84 + 65; hence not 73 divides 6197 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6197 & n is prime
  holds not n divides 6197 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
