
theorem
  6661 is prime
proof
  now
    6661 = 2*3330 + 1; hence not 2 divides 6661 by NAT_4:9;
    6661 = 3*2220 + 1; hence not 3 divides 6661 by NAT_4:9;
    6661 = 5*1332 + 1; hence not 5 divides 6661 by NAT_4:9;
    6661 = 7*951 + 4; hence not 7 divides 6661 by NAT_4:9;
    6661 = 11*605 + 6; hence not 11 divides 6661 by NAT_4:9;
    6661 = 13*512 + 5; hence not 13 divides 6661 by NAT_4:9;
    6661 = 17*391 + 14; hence not 17 divides 6661 by NAT_4:9;
    6661 = 19*350 + 11; hence not 19 divides 6661 by NAT_4:9;
    6661 = 23*289 + 14; hence not 23 divides 6661 by NAT_4:9;
    6661 = 29*229 + 20; hence not 29 divides 6661 by NAT_4:9;
    6661 = 31*214 + 27; hence not 31 divides 6661 by NAT_4:9;
    6661 = 37*180 + 1; hence not 37 divides 6661 by NAT_4:9;
    6661 = 41*162 + 19; hence not 41 divides 6661 by NAT_4:9;
    6661 = 43*154 + 39; hence not 43 divides 6661 by NAT_4:9;
    6661 = 47*141 + 34; hence not 47 divides 6661 by NAT_4:9;
    6661 = 53*125 + 36; hence not 53 divides 6661 by NAT_4:9;
    6661 = 59*112 + 53; hence not 59 divides 6661 by NAT_4:9;
    6661 = 61*109 + 12; hence not 61 divides 6661 by NAT_4:9;
    6661 = 67*99 + 28; hence not 67 divides 6661 by NAT_4:9;
    6661 = 71*93 + 58; hence not 71 divides 6661 by NAT_4:9;
    6661 = 73*91 + 18; hence not 73 divides 6661 by NAT_4:9;
    6661 = 79*84 + 25; hence not 79 divides 6661 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6661 & n is prime
  holds not n divides 6661 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
