
theorem
  9949 is prime
proof
  now
    9949 = 2*4974 + 1; hence not 2 divides 9949 by NAT_4:9;
    9949 = 3*3316 + 1; hence not 3 divides 9949 by NAT_4:9;
    9949 = 5*1989 + 4; hence not 5 divides 9949 by NAT_4:9;
    9949 = 7*1421 + 2; hence not 7 divides 9949 by NAT_4:9;
    9949 = 11*904 + 5; hence not 11 divides 9949 by NAT_4:9;
    9949 = 13*765 + 4; hence not 13 divides 9949 by NAT_4:9;
    9949 = 17*585 + 4; hence not 17 divides 9949 by NAT_4:9;
    9949 = 19*523 + 12; hence not 19 divides 9949 by NAT_4:9;
    9949 = 23*432 + 13; hence not 23 divides 9949 by NAT_4:9;
    9949 = 29*343 + 2; hence not 29 divides 9949 by NAT_4:9;
    9949 = 31*320 + 29; hence not 31 divides 9949 by NAT_4:9;
    9949 = 37*268 + 33; hence not 37 divides 9949 by NAT_4:9;
    9949 = 41*242 + 27; hence not 41 divides 9949 by NAT_4:9;
    9949 = 43*231 + 16; hence not 43 divides 9949 by NAT_4:9;
    9949 = 47*211 + 32; hence not 47 divides 9949 by NAT_4:9;
    9949 = 53*187 + 38; hence not 53 divides 9949 by NAT_4:9;
    9949 = 59*168 + 37; hence not 59 divides 9949 by NAT_4:9;
    9949 = 61*163 + 6; hence not 61 divides 9949 by NAT_4:9;
    9949 = 67*148 + 33; hence not 67 divides 9949 by NAT_4:9;
    9949 = 71*140 + 9; hence not 71 divides 9949 by NAT_4:9;
    9949 = 73*136 + 21; hence not 73 divides 9949 by NAT_4:9;
    9949 = 79*125 + 74; hence not 79 divides 9949 by NAT_4:9;
    9949 = 83*119 + 72; hence not 83 divides 9949 by NAT_4:9;
    9949 = 89*111 + 70; hence not 89 divides 9949 by NAT_4:9;
    9949 = 97*102 + 55; hence not 97 divides 9949 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9949 & n is prime
  holds not n divides 9949 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
