
theorem
  6691 is prime
proof
  now
    6691 = 2*3345 + 1; hence not 2 divides 6691 by NAT_4:9;
    6691 = 3*2230 + 1; hence not 3 divides 6691 by NAT_4:9;
    6691 = 5*1338 + 1; hence not 5 divides 6691 by NAT_4:9;
    6691 = 7*955 + 6; hence not 7 divides 6691 by NAT_4:9;
    6691 = 11*608 + 3; hence not 11 divides 6691 by NAT_4:9;
    6691 = 13*514 + 9; hence not 13 divides 6691 by NAT_4:9;
    6691 = 17*393 + 10; hence not 17 divides 6691 by NAT_4:9;
    6691 = 19*352 + 3; hence not 19 divides 6691 by NAT_4:9;
    6691 = 23*290 + 21; hence not 23 divides 6691 by NAT_4:9;
    6691 = 29*230 + 21; hence not 29 divides 6691 by NAT_4:9;
    6691 = 31*215 + 26; hence not 31 divides 6691 by NAT_4:9;
    6691 = 37*180 + 31; hence not 37 divides 6691 by NAT_4:9;
    6691 = 41*163 + 8; hence not 41 divides 6691 by NAT_4:9;
    6691 = 43*155 + 26; hence not 43 divides 6691 by NAT_4:9;
    6691 = 47*142 + 17; hence not 47 divides 6691 by NAT_4:9;
    6691 = 53*126 + 13; hence not 53 divides 6691 by NAT_4:9;
    6691 = 59*113 + 24; hence not 59 divides 6691 by NAT_4:9;
    6691 = 61*109 + 42; hence not 61 divides 6691 by NAT_4:9;
    6691 = 67*99 + 58; hence not 67 divides 6691 by NAT_4:9;
    6691 = 71*94 + 17; hence not 71 divides 6691 by NAT_4:9;
    6691 = 73*91 + 48; hence not 73 divides 6691 by NAT_4:9;
    6691 = 79*84 + 55; hence not 79 divides 6691 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6691 & n is prime
  holds not n divides 6691 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
