
theorem
  6619 is prime
proof
  now
    6619 = 2*3309 + 1; hence not 2 divides 6619 by NAT_4:9;
    6619 = 3*2206 + 1; hence not 3 divides 6619 by NAT_4:9;
    6619 = 5*1323 + 4; hence not 5 divides 6619 by NAT_4:9;
    6619 = 7*945 + 4; hence not 7 divides 6619 by NAT_4:9;
    6619 = 11*601 + 8; hence not 11 divides 6619 by NAT_4:9;
    6619 = 13*509 + 2; hence not 13 divides 6619 by NAT_4:9;
    6619 = 17*389 + 6; hence not 17 divides 6619 by NAT_4:9;
    6619 = 19*348 + 7; hence not 19 divides 6619 by NAT_4:9;
    6619 = 23*287 + 18; hence not 23 divides 6619 by NAT_4:9;
    6619 = 29*228 + 7; hence not 29 divides 6619 by NAT_4:9;
    6619 = 31*213 + 16; hence not 31 divides 6619 by NAT_4:9;
    6619 = 37*178 + 33; hence not 37 divides 6619 by NAT_4:9;
    6619 = 41*161 + 18; hence not 41 divides 6619 by NAT_4:9;
    6619 = 43*153 + 40; hence not 43 divides 6619 by NAT_4:9;
    6619 = 47*140 + 39; hence not 47 divides 6619 by NAT_4:9;
    6619 = 53*124 + 47; hence not 53 divides 6619 by NAT_4:9;
    6619 = 59*112 + 11; hence not 59 divides 6619 by NAT_4:9;
    6619 = 61*108 + 31; hence not 61 divides 6619 by NAT_4:9;
    6619 = 67*98 + 53; hence not 67 divides 6619 by NAT_4:9;
    6619 = 71*93 + 16; hence not 71 divides 6619 by NAT_4:9;
    6619 = 73*90 + 49; hence not 73 divides 6619 by NAT_4:9;
    6619 = 79*83 + 62; hence not 79 divides 6619 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6619 & n is prime
  holds not n divides 6619 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
