
theorem
  5347 is prime
proof
  now
    5347 = 2*2673 + 1; hence not 2 divides 5347 by NAT_4:9;
    5347 = 3*1782 + 1; hence not 3 divides 5347 by NAT_4:9;
    5347 = 5*1069 + 2; hence not 5 divides 5347 by NAT_4:9;
    5347 = 7*763 + 6; hence not 7 divides 5347 by NAT_4:9;
    5347 = 11*486 + 1; hence not 11 divides 5347 by NAT_4:9;
    5347 = 13*411 + 4; hence not 13 divides 5347 by NAT_4:9;
    5347 = 17*314 + 9; hence not 17 divides 5347 by NAT_4:9;
    5347 = 19*281 + 8; hence not 19 divides 5347 by NAT_4:9;
    5347 = 23*232 + 11; hence not 23 divides 5347 by NAT_4:9;
    5347 = 29*184 + 11; hence not 29 divides 5347 by NAT_4:9;
    5347 = 31*172 + 15; hence not 31 divides 5347 by NAT_4:9;
    5347 = 37*144 + 19; hence not 37 divides 5347 by NAT_4:9;
    5347 = 41*130 + 17; hence not 41 divides 5347 by NAT_4:9;
    5347 = 43*124 + 15; hence not 43 divides 5347 by NAT_4:9;
    5347 = 47*113 + 36; hence not 47 divides 5347 by NAT_4:9;
    5347 = 53*100 + 47; hence not 53 divides 5347 by NAT_4:9;
    5347 = 59*90 + 37; hence not 59 divides 5347 by NAT_4:9;
    5347 = 61*87 + 40; hence not 61 divides 5347 by NAT_4:9;
    5347 = 67*79 + 54; hence not 67 divides 5347 by NAT_4:9;
    5347 = 71*75 + 22; hence not 71 divides 5347 by NAT_4:9;
    5347 = 73*73 + 18; hence not 73 divides 5347 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5347 & n is prime
  holds not n divides 5347 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
