
theorem
  7309 is prime
proof
  now
    7309 = 2*3654 + 1; hence not 2 divides 7309 by NAT_4:9;
    7309 = 3*2436 + 1; hence not 3 divides 7309 by NAT_4:9;
    7309 = 5*1461 + 4; hence not 5 divides 7309 by NAT_4:9;
    7309 = 7*1044 + 1; hence not 7 divides 7309 by NAT_4:9;
    7309 = 11*664 + 5; hence not 11 divides 7309 by NAT_4:9;
    7309 = 13*562 + 3; hence not 13 divides 7309 by NAT_4:9;
    7309 = 17*429 + 16; hence not 17 divides 7309 by NAT_4:9;
    7309 = 19*384 + 13; hence not 19 divides 7309 by NAT_4:9;
    7309 = 23*317 + 18; hence not 23 divides 7309 by NAT_4:9;
    7309 = 29*252 + 1; hence not 29 divides 7309 by NAT_4:9;
    7309 = 31*235 + 24; hence not 31 divides 7309 by NAT_4:9;
    7309 = 37*197 + 20; hence not 37 divides 7309 by NAT_4:9;
    7309 = 41*178 + 11; hence not 41 divides 7309 by NAT_4:9;
    7309 = 43*169 + 42; hence not 43 divides 7309 by NAT_4:9;
    7309 = 47*155 + 24; hence not 47 divides 7309 by NAT_4:9;
    7309 = 53*137 + 48; hence not 53 divides 7309 by NAT_4:9;
    7309 = 59*123 + 52; hence not 59 divides 7309 by NAT_4:9;
    7309 = 61*119 + 50; hence not 61 divides 7309 by NAT_4:9;
    7309 = 67*109 + 6; hence not 67 divides 7309 by NAT_4:9;
    7309 = 71*102 + 67; hence not 71 divides 7309 by NAT_4:9;
    7309 = 73*100 + 9; hence not 73 divides 7309 by NAT_4:9;
    7309 = 79*92 + 41; hence not 79 divides 7309 by NAT_4:9;
    7309 = 83*88 + 5; hence not 83 divides 7309 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7309 & n is prime
  holds not n divides 7309 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
