
theorem
  9901 is prime
proof
  now
    9901 = 2*4950 + 1; hence not 2 divides 9901 by NAT_4:9;
    9901 = 3*3300 + 1; hence not 3 divides 9901 by NAT_4:9;
    9901 = 5*1980 + 1; hence not 5 divides 9901 by NAT_4:9;
    9901 = 7*1414 + 3; hence not 7 divides 9901 by NAT_4:9;
    9901 = 11*900 + 1; hence not 11 divides 9901 by NAT_4:9;
    9901 = 13*761 + 8; hence not 13 divides 9901 by NAT_4:9;
    9901 = 17*582 + 7; hence not 17 divides 9901 by NAT_4:9;
    9901 = 19*521 + 2; hence not 19 divides 9901 by NAT_4:9;
    9901 = 23*430 + 11; hence not 23 divides 9901 by NAT_4:9;
    9901 = 29*341 + 12; hence not 29 divides 9901 by NAT_4:9;
    9901 = 31*319 + 12; hence not 31 divides 9901 by NAT_4:9;
    9901 = 37*267 + 22; hence not 37 divides 9901 by NAT_4:9;
    9901 = 41*241 + 20; hence not 41 divides 9901 by NAT_4:9;
    9901 = 43*230 + 11; hence not 43 divides 9901 by NAT_4:9;
    9901 = 47*210 + 31; hence not 47 divides 9901 by NAT_4:9;
    9901 = 53*186 + 43; hence not 53 divides 9901 by NAT_4:9;
    9901 = 59*167 + 48; hence not 59 divides 9901 by NAT_4:9;
    9901 = 61*162 + 19; hence not 61 divides 9901 by NAT_4:9;
    9901 = 67*147 + 52; hence not 67 divides 9901 by NAT_4:9;
    9901 = 71*139 + 32; hence not 71 divides 9901 by NAT_4:9;
    9901 = 73*135 + 46; hence not 73 divides 9901 by NAT_4:9;
    9901 = 79*125 + 26; hence not 79 divides 9901 by NAT_4:9;
    9901 = 83*119 + 24; hence not 83 divides 9901 by NAT_4:9;
    9901 = 89*111 + 22; hence not 89 divides 9901 by NAT_4:9;
    9901 = 97*102 + 7; hence not 97 divides 9901 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9901 & n is prime
  holds not n divides 9901 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
