
theorem
  6899 is prime
proof
  now
    6899 = 2*3449 + 1; hence not 2 divides 6899 by NAT_4:9;
    6899 = 3*2299 + 2; hence not 3 divides 6899 by NAT_4:9;
    6899 = 5*1379 + 4; hence not 5 divides 6899 by NAT_4:9;
    6899 = 7*985 + 4; hence not 7 divides 6899 by NAT_4:9;
    6899 = 11*627 + 2; hence not 11 divides 6899 by NAT_4:9;
    6899 = 13*530 + 9; hence not 13 divides 6899 by NAT_4:9;
    6899 = 17*405 + 14; hence not 17 divides 6899 by NAT_4:9;
    6899 = 19*363 + 2; hence not 19 divides 6899 by NAT_4:9;
    6899 = 23*299 + 22; hence not 23 divides 6899 by NAT_4:9;
    6899 = 29*237 + 26; hence not 29 divides 6899 by NAT_4:9;
    6899 = 31*222 + 17; hence not 31 divides 6899 by NAT_4:9;
    6899 = 37*186 + 17; hence not 37 divides 6899 by NAT_4:9;
    6899 = 41*168 + 11; hence not 41 divides 6899 by NAT_4:9;
    6899 = 43*160 + 19; hence not 43 divides 6899 by NAT_4:9;
    6899 = 47*146 + 37; hence not 47 divides 6899 by NAT_4:9;
    6899 = 53*130 + 9; hence not 53 divides 6899 by NAT_4:9;
    6899 = 59*116 + 55; hence not 59 divides 6899 by NAT_4:9;
    6899 = 61*113 + 6; hence not 61 divides 6899 by NAT_4:9;
    6899 = 67*102 + 65; hence not 67 divides 6899 by NAT_4:9;
    6899 = 71*97 + 12; hence not 71 divides 6899 by NAT_4:9;
    6899 = 73*94 + 37; hence not 73 divides 6899 by NAT_4:9;
    6899 = 79*87 + 26; hence not 79 divides 6899 by NAT_4:9;
    6899 = 83*83 + 10; hence not 83 divides 6899 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6899 & n is prime
  holds not n divides 6899 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
