
theorem
  6701 is prime
proof
  now
    6701 = 2*3350 + 1; hence not 2 divides 6701 by NAT_4:9;
    6701 = 3*2233 + 2; hence not 3 divides 6701 by NAT_4:9;
    6701 = 5*1340 + 1; hence not 5 divides 6701 by NAT_4:9;
    6701 = 7*957 + 2; hence not 7 divides 6701 by NAT_4:9;
    6701 = 11*609 + 2; hence not 11 divides 6701 by NAT_4:9;
    6701 = 13*515 + 6; hence not 13 divides 6701 by NAT_4:9;
    6701 = 17*394 + 3; hence not 17 divides 6701 by NAT_4:9;
    6701 = 19*352 + 13; hence not 19 divides 6701 by NAT_4:9;
    6701 = 23*291 + 8; hence not 23 divides 6701 by NAT_4:9;
    6701 = 29*231 + 2; hence not 29 divides 6701 by NAT_4:9;
    6701 = 31*216 + 5; hence not 31 divides 6701 by NAT_4:9;
    6701 = 37*181 + 4; hence not 37 divides 6701 by NAT_4:9;
    6701 = 41*163 + 18; hence not 41 divides 6701 by NAT_4:9;
    6701 = 43*155 + 36; hence not 43 divides 6701 by NAT_4:9;
    6701 = 47*142 + 27; hence not 47 divides 6701 by NAT_4:9;
    6701 = 53*126 + 23; hence not 53 divides 6701 by NAT_4:9;
    6701 = 59*113 + 34; hence not 59 divides 6701 by NAT_4:9;
    6701 = 61*109 + 52; hence not 61 divides 6701 by NAT_4:9;
    6701 = 67*100 + 1; hence not 67 divides 6701 by NAT_4:9;
    6701 = 71*94 + 27; hence not 71 divides 6701 by NAT_4:9;
    6701 = 73*91 + 58; hence not 73 divides 6701 by NAT_4:9;
    6701 = 79*84 + 65; hence not 79 divides 6701 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6701 & n is prime
  holds not n divides 6701 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
