
theorem
  8059 is prime
proof
  now
    8059 = 2*4029 + 1; hence not 2 divides 8059 by NAT_4:9;
    8059 = 3*2686 + 1; hence not 3 divides 8059 by NAT_4:9;
    8059 = 5*1611 + 4; hence not 5 divides 8059 by NAT_4:9;
    8059 = 7*1151 + 2; hence not 7 divides 8059 by NAT_4:9;
    8059 = 11*732 + 7; hence not 11 divides 8059 by NAT_4:9;
    8059 = 13*619 + 12; hence not 13 divides 8059 by NAT_4:9;
    8059 = 17*474 + 1; hence not 17 divides 8059 by NAT_4:9;
    8059 = 19*424 + 3; hence not 19 divides 8059 by NAT_4:9;
    8059 = 23*350 + 9; hence not 23 divides 8059 by NAT_4:9;
    8059 = 29*277 + 26; hence not 29 divides 8059 by NAT_4:9;
    8059 = 31*259 + 30; hence not 31 divides 8059 by NAT_4:9;
    8059 = 37*217 + 30; hence not 37 divides 8059 by NAT_4:9;
    8059 = 41*196 + 23; hence not 41 divides 8059 by NAT_4:9;
    8059 = 43*187 + 18; hence not 43 divides 8059 by NAT_4:9;
    8059 = 47*171 + 22; hence not 47 divides 8059 by NAT_4:9;
    8059 = 53*152 + 3; hence not 53 divides 8059 by NAT_4:9;
    8059 = 59*136 + 35; hence not 59 divides 8059 by NAT_4:9;
    8059 = 61*132 + 7; hence not 61 divides 8059 by NAT_4:9;
    8059 = 67*120 + 19; hence not 67 divides 8059 by NAT_4:9;
    8059 = 71*113 + 36; hence not 71 divides 8059 by NAT_4:9;
    8059 = 73*110 + 29; hence not 73 divides 8059 by NAT_4:9;
    8059 = 79*102 + 1; hence not 79 divides 8059 by NAT_4:9;
    8059 = 83*97 + 8; hence not 83 divides 8059 by NAT_4:9;
    8059 = 89*90 + 49; hence not 89 divides 8059 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8059 & n is prime
  holds not n divides 8059 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
