
theorem
  6841 is prime
proof
  now
    6841 = 2*3420 + 1; hence not 2 divides 6841 by NAT_4:9;
    6841 = 3*2280 + 1; hence not 3 divides 6841 by NAT_4:9;
    6841 = 5*1368 + 1; hence not 5 divides 6841 by NAT_4:9;
    6841 = 7*977 + 2; hence not 7 divides 6841 by NAT_4:9;
    6841 = 11*621 + 10; hence not 11 divides 6841 by NAT_4:9;
    6841 = 13*526 + 3; hence not 13 divides 6841 by NAT_4:9;
    6841 = 17*402 + 7; hence not 17 divides 6841 by NAT_4:9;
    6841 = 19*360 + 1; hence not 19 divides 6841 by NAT_4:9;
    6841 = 23*297 + 10; hence not 23 divides 6841 by NAT_4:9;
    6841 = 29*235 + 26; hence not 29 divides 6841 by NAT_4:9;
    6841 = 31*220 + 21; hence not 31 divides 6841 by NAT_4:9;
    6841 = 37*184 + 33; hence not 37 divides 6841 by NAT_4:9;
    6841 = 41*166 + 35; hence not 41 divides 6841 by NAT_4:9;
    6841 = 43*159 + 4; hence not 43 divides 6841 by NAT_4:9;
    6841 = 47*145 + 26; hence not 47 divides 6841 by NAT_4:9;
    6841 = 53*129 + 4; hence not 53 divides 6841 by NAT_4:9;
    6841 = 59*115 + 56; hence not 59 divides 6841 by NAT_4:9;
    6841 = 61*112 + 9; hence not 61 divides 6841 by NAT_4:9;
    6841 = 67*102 + 7; hence not 67 divides 6841 by NAT_4:9;
    6841 = 71*96 + 25; hence not 71 divides 6841 by NAT_4:9;
    6841 = 73*93 + 52; hence not 73 divides 6841 by NAT_4:9;
    6841 = 79*86 + 47; hence not 79 divides 6841 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6841 & n is prime
  holds not n divides 6841 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
