
theorem
  4973 is prime
proof
  now
    4973 = 2*2486 + 1; hence not 2 divides 4973 by NAT_4:9;
    4973 = 3*1657 + 2; hence not 3 divides 4973 by NAT_4:9;
    4973 = 5*994 + 3; hence not 5 divides 4973 by NAT_4:9;
    4973 = 7*710 + 3; hence not 7 divides 4973 by NAT_4:9;
    4973 = 11*452 + 1; hence not 11 divides 4973 by NAT_4:9;
    4973 = 13*382 + 7; hence not 13 divides 4973 by NAT_4:9;
    4973 = 17*292 + 9; hence not 17 divides 4973 by NAT_4:9;
    4973 = 19*261 + 14; hence not 19 divides 4973 by NAT_4:9;
    4973 = 23*216 + 5; hence not 23 divides 4973 by NAT_4:9;
    4973 = 29*171 + 14; hence not 29 divides 4973 by NAT_4:9;
    4973 = 31*160 + 13; hence not 31 divides 4973 by NAT_4:9;
    4973 = 37*134 + 15; hence not 37 divides 4973 by NAT_4:9;
    4973 = 41*121 + 12; hence not 41 divides 4973 by NAT_4:9;
    4973 = 43*115 + 28; hence not 43 divides 4973 by NAT_4:9;
    4973 = 47*105 + 38; hence not 47 divides 4973 by NAT_4:9;
    4973 = 53*93 + 44; hence not 53 divides 4973 by NAT_4:9;
    4973 = 59*84 + 17; hence not 59 divides 4973 by NAT_4:9;
    4973 = 61*81 + 32; hence not 61 divides 4973 by NAT_4:9;
    4973 = 67*74 + 15; hence not 67 divides 4973 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4973 & n is prime
  holds not n divides 4973 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
