
theorem
  9931 is prime
proof
  now
    9931 = 2*4965 + 1; hence not 2 divides 9931 by NAT_4:9;
    9931 = 3*3310 + 1; hence not 3 divides 9931 by NAT_4:9;
    9931 = 5*1986 + 1; hence not 5 divides 9931 by NAT_4:9;
    9931 = 7*1418 + 5; hence not 7 divides 9931 by NAT_4:9;
    9931 = 11*902 + 9; hence not 11 divides 9931 by NAT_4:9;
    9931 = 13*763 + 12; hence not 13 divides 9931 by NAT_4:9;
    9931 = 17*584 + 3; hence not 17 divides 9931 by NAT_4:9;
    9931 = 19*522 + 13; hence not 19 divides 9931 by NAT_4:9;
    9931 = 23*431 + 18; hence not 23 divides 9931 by NAT_4:9;
    9931 = 29*342 + 13; hence not 29 divides 9931 by NAT_4:9;
    9931 = 31*320 + 11; hence not 31 divides 9931 by NAT_4:9;
    9931 = 37*268 + 15; hence not 37 divides 9931 by NAT_4:9;
    9931 = 41*242 + 9; hence not 41 divides 9931 by NAT_4:9;
    9931 = 43*230 + 41; hence not 43 divides 9931 by NAT_4:9;
    9931 = 47*211 + 14; hence not 47 divides 9931 by NAT_4:9;
    9931 = 53*187 + 20; hence not 53 divides 9931 by NAT_4:9;
    9931 = 59*168 + 19; hence not 59 divides 9931 by NAT_4:9;
    9931 = 61*162 + 49; hence not 61 divides 9931 by NAT_4:9;
    9931 = 67*148 + 15; hence not 67 divides 9931 by NAT_4:9;
    9931 = 71*139 + 62; hence not 71 divides 9931 by NAT_4:9;
    9931 = 73*136 + 3; hence not 73 divides 9931 by NAT_4:9;
    9931 = 79*125 + 56; hence not 79 divides 9931 by NAT_4:9;
    9931 = 83*119 + 54; hence not 83 divides 9931 by NAT_4:9;
    9931 = 89*111 + 52; hence not 89 divides 9931 by NAT_4:9;
    9931 = 97*102 + 37; hence not 97 divides 9931 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9931 & n is prime
  holds not n divides 9931 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
