
theorem
  8293 is prime
proof
  now
    8293 = 2*4146 + 1; hence not 2 divides 8293 by NAT_4:9;
    8293 = 3*2764 + 1; hence not 3 divides 8293 by NAT_4:9;
    8293 = 5*1658 + 3; hence not 5 divides 8293 by NAT_4:9;
    8293 = 7*1184 + 5; hence not 7 divides 8293 by NAT_4:9;
    8293 = 11*753 + 10; hence not 11 divides 8293 by NAT_4:9;
    8293 = 13*637 + 12; hence not 13 divides 8293 by NAT_4:9;
    8293 = 17*487 + 14; hence not 17 divides 8293 by NAT_4:9;
    8293 = 19*436 + 9; hence not 19 divides 8293 by NAT_4:9;
    8293 = 23*360 + 13; hence not 23 divides 8293 by NAT_4:9;
    8293 = 29*285 + 28; hence not 29 divides 8293 by NAT_4:9;
    8293 = 31*267 + 16; hence not 31 divides 8293 by NAT_4:9;
    8293 = 37*224 + 5; hence not 37 divides 8293 by NAT_4:9;
    8293 = 41*202 + 11; hence not 41 divides 8293 by NAT_4:9;
    8293 = 43*192 + 37; hence not 43 divides 8293 by NAT_4:9;
    8293 = 47*176 + 21; hence not 47 divides 8293 by NAT_4:9;
    8293 = 53*156 + 25; hence not 53 divides 8293 by NAT_4:9;
    8293 = 59*140 + 33; hence not 59 divides 8293 by NAT_4:9;
    8293 = 61*135 + 58; hence not 61 divides 8293 by NAT_4:9;
    8293 = 67*123 + 52; hence not 67 divides 8293 by NAT_4:9;
    8293 = 71*116 + 57; hence not 71 divides 8293 by NAT_4:9;
    8293 = 73*113 + 44; hence not 73 divides 8293 by NAT_4:9;
    8293 = 79*104 + 77; hence not 79 divides 8293 by NAT_4:9;
    8293 = 83*99 + 76; hence not 83 divides 8293 by NAT_4:9;
    8293 = 89*93 + 16; hence not 89 divides 8293 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8293 & n is prime
  holds not n divides 8293 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
