
theorem
  6599 is prime
proof
  now
    6599 = 2*3299 + 1; hence not 2 divides 6599 by NAT_4:9;
    6599 = 3*2199 + 2; hence not 3 divides 6599 by NAT_4:9;
    6599 = 5*1319 + 4; hence not 5 divides 6599 by NAT_4:9;
    6599 = 7*942 + 5; hence not 7 divides 6599 by NAT_4:9;
    6599 = 11*599 + 10; hence not 11 divides 6599 by NAT_4:9;
    6599 = 13*507 + 8; hence not 13 divides 6599 by NAT_4:9;
    6599 = 17*388 + 3; hence not 17 divides 6599 by NAT_4:9;
    6599 = 19*347 + 6; hence not 19 divides 6599 by NAT_4:9;
    6599 = 23*286 + 21; hence not 23 divides 6599 by NAT_4:9;
    6599 = 29*227 + 16; hence not 29 divides 6599 by NAT_4:9;
    6599 = 31*212 + 27; hence not 31 divides 6599 by NAT_4:9;
    6599 = 37*178 + 13; hence not 37 divides 6599 by NAT_4:9;
    6599 = 41*160 + 39; hence not 41 divides 6599 by NAT_4:9;
    6599 = 43*153 + 20; hence not 43 divides 6599 by NAT_4:9;
    6599 = 47*140 + 19; hence not 47 divides 6599 by NAT_4:9;
    6599 = 53*124 + 27; hence not 53 divides 6599 by NAT_4:9;
    6599 = 59*111 + 50; hence not 59 divides 6599 by NAT_4:9;
    6599 = 61*108 + 11; hence not 61 divides 6599 by NAT_4:9;
    6599 = 67*98 + 33; hence not 67 divides 6599 by NAT_4:9;
    6599 = 71*92 + 67; hence not 71 divides 6599 by NAT_4:9;
    6599 = 73*90 + 29; hence not 73 divides 6599 by NAT_4:9;
    6599 = 79*83 + 42; hence not 79 divides 6599 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6599 & n is prime
  holds not n divides 6599 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
