
theorem
  6659 is prime
proof
  now
    6659 = 2*3329 + 1; hence not 2 divides 6659 by NAT_4:9;
    6659 = 3*2219 + 2; hence not 3 divides 6659 by NAT_4:9;
    6659 = 5*1331 + 4; hence not 5 divides 6659 by NAT_4:9;
    6659 = 7*951 + 2; hence not 7 divides 6659 by NAT_4:9;
    6659 = 11*605 + 4; hence not 11 divides 6659 by NAT_4:9;
    6659 = 13*512 + 3; hence not 13 divides 6659 by NAT_4:9;
    6659 = 17*391 + 12; hence not 17 divides 6659 by NAT_4:9;
    6659 = 19*350 + 9; hence not 19 divides 6659 by NAT_4:9;
    6659 = 23*289 + 12; hence not 23 divides 6659 by NAT_4:9;
    6659 = 29*229 + 18; hence not 29 divides 6659 by NAT_4:9;
    6659 = 31*214 + 25; hence not 31 divides 6659 by NAT_4:9;
    6659 = 37*179 + 36; hence not 37 divides 6659 by NAT_4:9;
    6659 = 41*162 + 17; hence not 41 divides 6659 by NAT_4:9;
    6659 = 43*154 + 37; hence not 43 divides 6659 by NAT_4:9;
    6659 = 47*141 + 32; hence not 47 divides 6659 by NAT_4:9;
    6659 = 53*125 + 34; hence not 53 divides 6659 by NAT_4:9;
    6659 = 59*112 + 51; hence not 59 divides 6659 by NAT_4:9;
    6659 = 61*109 + 10; hence not 61 divides 6659 by NAT_4:9;
    6659 = 67*99 + 26; hence not 67 divides 6659 by NAT_4:9;
    6659 = 71*93 + 56; hence not 71 divides 6659 by NAT_4:9;
    6659 = 73*91 + 16; hence not 73 divides 6659 by NAT_4:9;
    6659 = 79*84 + 23; hence not 79 divides 6659 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6659 & n is prime
  holds not n divides 6659 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
