
theorem
  4793 is prime
proof
  now
    4793 = 2*2396 + 1; hence not 2 divides 4793 by NAT_4:9;
    4793 = 3*1597 + 2; hence not 3 divides 4793 by NAT_4:9;
    4793 = 5*958 + 3; hence not 5 divides 4793 by NAT_4:9;
    4793 = 7*684 + 5; hence not 7 divides 4793 by NAT_4:9;
    4793 = 11*435 + 8; hence not 11 divides 4793 by NAT_4:9;
    4793 = 13*368 + 9; hence not 13 divides 4793 by NAT_4:9;
    4793 = 17*281 + 16; hence not 17 divides 4793 by NAT_4:9;
    4793 = 19*252 + 5; hence not 19 divides 4793 by NAT_4:9;
    4793 = 23*208 + 9; hence not 23 divides 4793 by NAT_4:9;
    4793 = 29*165 + 8; hence not 29 divides 4793 by NAT_4:9;
    4793 = 31*154 + 19; hence not 31 divides 4793 by NAT_4:9;
    4793 = 37*129 + 20; hence not 37 divides 4793 by NAT_4:9;
    4793 = 41*116 + 37; hence not 41 divides 4793 by NAT_4:9;
    4793 = 43*111 + 20; hence not 43 divides 4793 by NAT_4:9;
    4793 = 47*101 + 46; hence not 47 divides 4793 by NAT_4:9;
    4793 = 53*90 + 23; hence not 53 divides 4793 by NAT_4:9;
    4793 = 59*81 + 14; hence not 59 divides 4793 by NAT_4:9;
    4793 = 61*78 + 35; hence not 61 divides 4793 by NAT_4:9;
    4793 = 67*71 + 36; hence not 67 divides 4793 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4793 & n is prime
  holds not n divides 4793 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
