
theorem
  4831 is prime
proof
  now
    4831 = 2*2415 + 1; hence not 2 divides 4831 by NAT_4:9;
    4831 = 3*1610 + 1; hence not 3 divides 4831 by NAT_4:9;
    4831 = 5*966 + 1; hence not 5 divides 4831 by NAT_4:9;
    4831 = 7*690 + 1; hence not 7 divides 4831 by NAT_4:9;
    4831 = 11*439 + 2; hence not 11 divides 4831 by NAT_4:9;
    4831 = 13*371 + 8; hence not 13 divides 4831 by NAT_4:9;
    4831 = 17*284 + 3; hence not 17 divides 4831 by NAT_4:9;
    4831 = 19*254 + 5; hence not 19 divides 4831 by NAT_4:9;
    4831 = 23*210 + 1; hence not 23 divides 4831 by NAT_4:9;
    4831 = 29*166 + 17; hence not 29 divides 4831 by NAT_4:9;
    4831 = 31*155 + 26; hence not 31 divides 4831 by NAT_4:9;
    4831 = 37*130 + 21; hence not 37 divides 4831 by NAT_4:9;
    4831 = 41*117 + 34; hence not 41 divides 4831 by NAT_4:9;
    4831 = 43*112 + 15; hence not 43 divides 4831 by NAT_4:9;
    4831 = 47*102 + 37; hence not 47 divides 4831 by NAT_4:9;
    4831 = 53*91 + 8; hence not 53 divides 4831 by NAT_4:9;
    4831 = 59*81 + 52; hence not 59 divides 4831 by NAT_4:9;
    4831 = 61*79 + 12; hence not 61 divides 4831 by NAT_4:9;
    4831 = 67*72 + 7; hence not 67 divides 4831 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4831 & n is prime
  holds not n divides 4831 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
