
theorem
  7369 is prime
proof
  now
    7369 = 2*3684 + 1; hence not 2 divides 7369 by NAT_4:9;
    7369 = 3*2456 + 1; hence not 3 divides 7369 by NAT_4:9;
    7369 = 5*1473 + 4; hence not 5 divides 7369 by NAT_4:9;
    7369 = 7*1052 + 5; hence not 7 divides 7369 by NAT_4:9;
    7369 = 11*669 + 10; hence not 11 divides 7369 by NAT_4:9;
    7369 = 13*566 + 11; hence not 13 divides 7369 by NAT_4:9;
    7369 = 17*433 + 8; hence not 17 divides 7369 by NAT_4:9;
    7369 = 19*387 + 16; hence not 19 divides 7369 by NAT_4:9;
    7369 = 23*320 + 9; hence not 23 divides 7369 by NAT_4:9;
    7369 = 29*254 + 3; hence not 29 divides 7369 by NAT_4:9;
    7369 = 31*237 + 22; hence not 31 divides 7369 by NAT_4:9;
    7369 = 37*199 + 6; hence not 37 divides 7369 by NAT_4:9;
    7369 = 41*179 + 30; hence not 41 divides 7369 by NAT_4:9;
    7369 = 43*171 + 16; hence not 43 divides 7369 by NAT_4:9;
    7369 = 47*156 + 37; hence not 47 divides 7369 by NAT_4:9;
    7369 = 53*139 + 2; hence not 53 divides 7369 by NAT_4:9;
    7369 = 59*124 + 53; hence not 59 divides 7369 by NAT_4:9;
    7369 = 61*120 + 49; hence not 61 divides 7369 by NAT_4:9;
    7369 = 67*109 + 66; hence not 67 divides 7369 by NAT_4:9;
    7369 = 71*103 + 56; hence not 71 divides 7369 by NAT_4:9;
    7369 = 73*100 + 69; hence not 73 divides 7369 by NAT_4:9;
    7369 = 79*93 + 22; hence not 79 divides 7369 by NAT_4:9;
    7369 = 83*88 + 65; hence not 83 divides 7369 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7369 & n is prime
  holds not n divides 7369 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
