
theorem
  7349 is prime
proof
  now
    7349 = 2*3674 + 1; hence not 2 divides 7349 by NAT_4:9;
    7349 = 3*2449 + 2; hence not 3 divides 7349 by NAT_4:9;
    7349 = 5*1469 + 4; hence not 5 divides 7349 by NAT_4:9;
    7349 = 7*1049 + 6; hence not 7 divides 7349 by NAT_4:9;
    7349 = 11*668 + 1; hence not 11 divides 7349 by NAT_4:9;
    7349 = 13*565 + 4; hence not 13 divides 7349 by NAT_4:9;
    7349 = 17*432 + 5; hence not 17 divides 7349 by NAT_4:9;
    7349 = 19*386 + 15; hence not 19 divides 7349 by NAT_4:9;
    7349 = 23*319 + 12; hence not 23 divides 7349 by NAT_4:9;
    7349 = 29*253 + 12; hence not 29 divides 7349 by NAT_4:9;
    7349 = 31*237 + 2; hence not 31 divides 7349 by NAT_4:9;
    7349 = 37*198 + 23; hence not 37 divides 7349 by NAT_4:9;
    7349 = 41*179 + 10; hence not 41 divides 7349 by NAT_4:9;
    7349 = 43*170 + 39; hence not 43 divides 7349 by NAT_4:9;
    7349 = 47*156 + 17; hence not 47 divides 7349 by NAT_4:9;
    7349 = 53*138 + 35; hence not 53 divides 7349 by NAT_4:9;
    7349 = 59*124 + 33; hence not 59 divides 7349 by NAT_4:9;
    7349 = 61*120 + 29; hence not 61 divides 7349 by NAT_4:9;
    7349 = 67*109 + 46; hence not 67 divides 7349 by NAT_4:9;
    7349 = 71*103 + 36; hence not 71 divides 7349 by NAT_4:9;
    7349 = 73*100 + 49; hence not 73 divides 7349 by NAT_4:9;
    7349 = 79*93 + 2; hence not 79 divides 7349 by NAT_4:9;
    7349 = 83*88 + 45; hence not 83 divides 7349 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7349 & n is prime
  holds not n divides 7349 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
