
theorem
  8291 is prime
proof
  now
    8291 = 2*4145 + 1; hence not 2 divides 8291 by NAT_4:9;
    8291 = 3*2763 + 2; hence not 3 divides 8291 by NAT_4:9;
    8291 = 5*1658 + 1; hence not 5 divides 8291 by NAT_4:9;
    8291 = 7*1184 + 3; hence not 7 divides 8291 by NAT_4:9;
    8291 = 11*753 + 8; hence not 11 divides 8291 by NAT_4:9;
    8291 = 13*637 + 10; hence not 13 divides 8291 by NAT_4:9;
    8291 = 17*487 + 12; hence not 17 divides 8291 by NAT_4:9;
    8291 = 19*436 + 7; hence not 19 divides 8291 by NAT_4:9;
    8291 = 23*360 + 11; hence not 23 divides 8291 by NAT_4:9;
    8291 = 29*285 + 26; hence not 29 divides 8291 by NAT_4:9;
    8291 = 31*267 + 14; hence not 31 divides 8291 by NAT_4:9;
    8291 = 37*224 + 3; hence not 37 divides 8291 by NAT_4:9;
    8291 = 41*202 + 9; hence not 41 divides 8291 by NAT_4:9;
    8291 = 43*192 + 35; hence not 43 divides 8291 by NAT_4:9;
    8291 = 47*176 + 19; hence not 47 divides 8291 by NAT_4:9;
    8291 = 53*156 + 23; hence not 53 divides 8291 by NAT_4:9;
    8291 = 59*140 + 31; hence not 59 divides 8291 by NAT_4:9;
    8291 = 61*135 + 56; hence not 61 divides 8291 by NAT_4:9;
    8291 = 67*123 + 50; hence not 67 divides 8291 by NAT_4:9;
    8291 = 71*116 + 55; hence not 71 divides 8291 by NAT_4:9;
    8291 = 73*113 + 42; hence not 73 divides 8291 by NAT_4:9;
    8291 = 79*104 + 75; hence not 79 divides 8291 by NAT_4:9;
    8291 = 83*99 + 74; hence not 83 divides 8291 by NAT_4:9;
    8291 = 89*93 + 14; hence not 89 divides 8291 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8291 & n is prime
  holds not n divides 8291 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
