
theorem
  6607 is prime
proof
  now
    6607 = 2*3303 + 1; hence not 2 divides 6607 by NAT_4:9;
    6607 = 3*2202 + 1; hence not 3 divides 6607 by NAT_4:9;
    6607 = 5*1321 + 2; hence not 5 divides 6607 by NAT_4:9;
    6607 = 7*943 + 6; hence not 7 divides 6607 by NAT_4:9;
    6607 = 11*600 + 7; hence not 11 divides 6607 by NAT_4:9;
    6607 = 13*508 + 3; hence not 13 divides 6607 by NAT_4:9;
    6607 = 17*388 + 11; hence not 17 divides 6607 by NAT_4:9;
    6607 = 19*347 + 14; hence not 19 divides 6607 by NAT_4:9;
    6607 = 23*287 + 6; hence not 23 divides 6607 by NAT_4:9;
    6607 = 29*227 + 24; hence not 29 divides 6607 by NAT_4:9;
    6607 = 31*213 + 4; hence not 31 divides 6607 by NAT_4:9;
    6607 = 37*178 + 21; hence not 37 divides 6607 by NAT_4:9;
    6607 = 41*161 + 6; hence not 41 divides 6607 by NAT_4:9;
    6607 = 43*153 + 28; hence not 43 divides 6607 by NAT_4:9;
    6607 = 47*140 + 27; hence not 47 divides 6607 by NAT_4:9;
    6607 = 53*124 + 35; hence not 53 divides 6607 by NAT_4:9;
    6607 = 59*111 + 58; hence not 59 divides 6607 by NAT_4:9;
    6607 = 61*108 + 19; hence not 61 divides 6607 by NAT_4:9;
    6607 = 67*98 + 41; hence not 67 divides 6607 by NAT_4:9;
    6607 = 71*93 + 4; hence not 71 divides 6607 by NAT_4:9;
    6607 = 73*90 + 37; hence not 73 divides 6607 by NAT_4:9;
    6607 = 79*83 + 50; hence not 79 divides 6607 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6607 & n is prime
  holds not n divides 6607 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
