
theorem
  7307 is prime
proof
  now
    7307 = 2*3653 + 1; hence not 2 divides 7307 by NAT_4:9;
    7307 = 3*2435 + 2; hence not 3 divides 7307 by NAT_4:9;
    7307 = 5*1461 + 2; hence not 5 divides 7307 by NAT_4:9;
    7307 = 7*1043 + 6; hence not 7 divides 7307 by NAT_4:9;
    7307 = 11*664 + 3; hence not 11 divides 7307 by NAT_4:9;
    7307 = 13*562 + 1; hence not 13 divides 7307 by NAT_4:9;
    7307 = 17*429 + 14; hence not 17 divides 7307 by NAT_4:9;
    7307 = 19*384 + 11; hence not 19 divides 7307 by NAT_4:9;
    7307 = 23*317 + 16; hence not 23 divides 7307 by NAT_4:9;
    7307 = 29*251 + 28; hence not 29 divides 7307 by NAT_4:9;
    7307 = 31*235 + 22; hence not 31 divides 7307 by NAT_4:9;
    7307 = 37*197 + 18; hence not 37 divides 7307 by NAT_4:9;
    7307 = 41*178 + 9; hence not 41 divides 7307 by NAT_4:9;
    7307 = 43*169 + 40; hence not 43 divides 7307 by NAT_4:9;
    7307 = 47*155 + 22; hence not 47 divides 7307 by NAT_4:9;
    7307 = 53*137 + 46; hence not 53 divides 7307 by NAT_4:9;
    7307 = 59*123 + 50; hence not 59 divides 7307 by NAT_4:9;
    7307 = 61*119 + 48; hence not 61 divides 7307 by NAT_4:9;
    7307 = 67*109 + 4; hence not 67 divides 7307 by NAT_4:9;
    7307 = 71*102 + 65; hence not 71 divides 7307 by NAT_4:9;
    7307 = 73*100 + 7; hence not 73 divides 7307 by NAT_4:9;
    7307 = 79*92 + 39; hence not 79 divides 7307 by NAT_4:9;
    7307 = 83*88 + 3; hence not 83 divides 7307 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7307 & n is prime
  holds not n divides 7307 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
