
theorem
  7933 is prime
proof
  now
    7933 = 2*3966 + 1; hence not 2 divides 7933 by NAT_4:9;
    7933 = 3*2644 + 1; hence not 3 divides 7933 by NAT_4:9;
    7933 = 5*1586 + 3; hence not 5 divides 7933 by NAT_4:9;
    7933 = 7*1133 + 2; hence not 7 divides 7933 by NAT_4:9;
    7933 = 11*721 + 2; hence not 11 divides 7933 by NAT_4:9;
    7933 = 13*610 + 3; hence not 13 divides 7933 by NAT_4:9;
    7933 = 17*466 + 11; hence not 17 divides 7933 by NAT_4:9;
    7933 = 19*417 + 10; hence not 19 divides 7933 by NAT_4:9;
    7933 = 23*344 + 21; hence not 23 divides 7933 by NAT_4:9;
    7933 = 29*273 + 16; hence not 29 divides 7933 by NAT_4:9;
    7933 = 31*255 + 28; hence not 31 divides 7933 by NAT_4:9;
    7933 = 37*214 + 15; hence not 37 divides 7933 by NAT_4:9;
    7933 = 41*193 + 20; hence not 41 divides 7933 by NAT_4:9;
    7933 = 43*184 + 21; hence not 43 divides 7933 by NAT_4:9;
    7933 = 47*168 + 37; hence not 47 divides 7933 by NAT_4:9;
    7933 = 53*149 + 36; hence not 53 divides 7933 by NAT_4:9;
    7933 = 59*134 + 27; hence not 59 divides 7933 by NAT_4:9;
    7933 = 61*130 + 3; hence not 61 divides 7933 by NAT_4:9;
    7933 = 67*118 + 27; hence not 67 divides 7933 by NAT_4:9;
    7933 = 71*111 + 52; hence not 71 divides 7933 by NAT_4:9;
    7933 = 73*108 + 49; hence not 73 divides 7933 by NAT_4:9;
    7933 = 79*100 + 33; hence not 79 divides 7933 by NAT_4:9;
    7933 = 83*95 + 48; hence not 83 divides 7933 by NAT_4:9;
    7933 = 89*89 + 12; hence not 89 divides 7933 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7933 & n is prime
  holds not n divides 7933 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
