
theorem
  8069 is prime
proof
  now
    8069 = 2*4034 + 1; hence not 2 divides 8069 by NAT_4:9;
    8069 = 3*2689 + 2; hence not 3 divides 8069 by NAT_4:9;
    8069 = 5*1613 + 4; hence not 5 divides 8069 by NAT_4:9;
    8069 = 7*1152 + 5; hence not 7 divides 8069 by NAT_4:9;
    8069 = 11*733 + 6; hence not 11 divides 8069 by NAT_4:9;
    8069 = 13*620 + 9; hence not 13 divides 8069 by NAT_4:9;
    8069 = 17*474 + 11; hence not 17 divides 8069 by NAT_4:9;
    8069 = 19*424 + 13; hence not 19 divides 8069 by NAT_4:9;
    8069 = 23*350 + 19; hence not 23 divides 8069 by NAT_4:9;
    8069 = 29*278 + 7; hence not 29 divides 8069 by NAT_4:9;
    8069 = 31*260 + 9; hence not 31 divides 8069 by NAT_4:9;
    8069 = 37*218 + 3; hence not 37 divides 8069 by NAT_4:9;
    8069 = 41*196 + 33; hence not 41 divides 8069 by NAT_4:9;
    8069 = 43*187 + 28; hence not 43 divides 8069 by NAT_4:9;
    8069 = 47*171 + 32; hence not 47 divides 8069 by NAT_4:9;
    8069 = 53*152 + 13; hence not 53 divides 8069 by NAT_4:9;
    8069 = 59*136 + 45; hence not 59 divides 8069 by NAT_4:9;
    8069 = 61*132 + 17; hence not 61 divides 8069 by NAT_4:9;
    8069 = 67*120 + 29; hence not 67 divides 8069 by NAT_4:9;
    8069 = 71*113 + 46; hence not 71 divides 8069 by NAT_4:9;
    8069 = 73*110 + 39; hence not 73 divides 8069 by NAT_4:9;
    8069 = 79*102 + 11; hence not 79 divides 8069 by NAT_4:9;
    8069 = 83*97 + 18; hence not 83 divides 8069 by NAT_4:9;
    8069 = 89*90 + 59; hence not 89 divides 8069 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8069 & n is prime
  holds not n divides 8069 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
