
theorem
  4993 is prime
proof
  now
    4993 = 2*2496 + 1; hence not 2 divides 4993 by NAT_4:9;
    4993 = 3*1664 + 1; hence not 3 divides 4993 by NAT_4:9;
    4993 = 5*998 + 3; hence not 5 divides 4993 by NAT_4:9;
    4993 = 7*713 + 2; hence not 7 divides 4993 by NAT_4:9;
    4993 = 11*453 + 10; hence not 11 divides 4993 by NAT_4:9;
    4993 = 13*384 + 1; hence not 13 divides 4993 by NAT_4:9;
    4993 = 17*293 + 12; hence not 17 divides 4993 by NAT_4:9;
    4993 = 19*262 + 15; hence not 19 divides 4993 by NAT_4:9;
    4993 = 23*217 + 2; hence not 23 divides 4993 by NAT_4:9;
    4993 = 29*172 + 5; hence not 29 divides 4993 by NAT_4:9;
    4993 = 31*161 + 2; hence not 31 divides 4993 by NAT_4:9;
    4993 = 37*134 + 35; hence not 37 divides 4993 by NAT_4:9;
    4993 = 41*121 + 32; hence not 41 divides 4993 by NAT_4:9;
    4993 = 43*116 + 5; hence not 43 divides 4993 by NAT_4:9;
    4993 = 47*106 + 11; hence not 47 divides 4993 by NAT_4:9;
    4993 = 53*94 + 11; hence not 53 divides 4993 by NAT_4:9;
    4993 = 59*84 + 37; hence not 59 divides 4993 by NAT_4:9;
    4993 = 61*81 + 52; hence not 61 divides 4993 by NAT_4:9;
    4993 = 67*74 + 35; hence not 67 divides 4993 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4993 & n is prime
  holds not n divides 4993 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
