
theorem
  4943 is prime
proof
  now
    4943 = 2*2471 + 1; hence not 2 divides 4943 by NAT_4:9;
    4943 = 3*1647 + 2; hence not 3 divides 4943 by NAT_4:9;
    4943 = 5*988 + 3; hence not 5 divides 4943 by NAT_4:9;
    4943 = 7*706 + 1; hence not 7 divides 4943 by NAT_4:9;
    4943 = 11*449 + 4; hence not 11 divides 4943 by NAT_4:9;
    4943 = 13*380 + 3; hence not 13 divides 4943 by NAT_4:9;
    4943 = 17*290 + 13; hence not 17 divides 4943 by NAT_4:9;
    4943 = 19*260 + 3; hence not 19 divides 4943 by NAT_4:9;
    4943 = 23*214 + 21; hence not 23 divides 4943 by NAT_4:9;
    4943 = 29*170 + 13; hence not 29 divides 4943 by NAT_4:9;
    4943 = 31*159 + 14; hence not 31 divides 4943 by NAT_4:9;
    4943 = 37*133 + 22; hence not 37 divides 4943 by NAT_4:9;
    4943 = 41*120 + 23; hence not 41 divides 4943 by NAT_4:9;
    4943 = 43*114 + 41; hence not 43 divides 4943 by NAT_4:9;
    4943 = 47*105 + 8; hence not 47 divides 4943 by NAT_4:9;
    4943 = 53*93 + 14; hence not 53 divides 4943 by NAT_4:9;
    4943 = 59*83 + 46; hence not 59 divides 4943 by NAT_4:9;
    4943 = 61*81 + 2; hence not 61 divides 4943 by NAT_4:9;
    4943 = 67*73 + 52; hence not 67 divides 4943 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4943 & n is prime
  holds not n divides 4943 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
