
theorem
  4999 is prime
proof
  now
    4999 = 2*2499 + 1; hence not 2 divides 4999 by NAT_4:9;
    4999 = 3*1666 + 1; hence not 3 divides 4999 by NAT_4:9;
    4999 = 5*999 + 4; hence not 5 divides 4999 by NAT_4:9;
    4999 = 7*714 + 1; hence not 7 divides 4999 by NAT_4:9;
    4999 = 11*454 + 5; hence not 11 divides 4999 by NAT_4:9;
    4999 = 13*384 + 7; hence not 13 divides 4999 by NAT_4:9;
    4999 = 17*294 + 1; hence not 17 divides 4999 by NAT_4:9;
    4999 = 19*263 + 2; hence not 19 divides 4999 by NAT_4:9;
    4999 = 23*217 + 8; hence not 23 divides 4999 by NAT_4:9;
    4999 = 29*172 + 11; hence not 29 divides 4999 by NAT_4:9;
    4999 = 31*161 + 8; hence not 31 divides 4999 by NAT_4:9;
    4999 = 37*135 + 4; hence not 37 divides 4999 by NAT_4:9;
    4999 = 41*121 + 38; hence not 41 divides 4999 by NAT_4:9;
    4999 = 43*116 + 11; hence not 43 divides 4999 by NAT_4:9;
    4999 = 47*106 + 17; hence not 47 divides 4999 by NAT_4:9;
    4999 = 53*94 + 17; hence not 53 divides 4999 by NAT_4:9;
    4999 = 59*84 + 43; hence not 59 divides 4999 by NAT_4:9;
    4999 = 61*81 + 58; hence not 61 divides 4999 by NAT_4:9;
    4999 = 67*74 + 41; hence not 67 divides 4999 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4999 & n is prime
  holds not n divides 4999 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
