
theorem
  8081 is prime
proof
  now
    8081 = 2*4040 + 1; hence not 2 divides 8081 by NAT_4:9;
    8081 = 3*2693 + 2; hence not 3 divides 8081 by NAT_4:9;
    8081 = 5*1616 + 1; hence not 5 divides 8081 by NAT_4:9;
    8081 = 7*1154 + 3; hence not 7 divides 8081 by NAT_4:9;
    8081 = 11*734 + 7; hence not 11 divides 8081 by NAT_4:9;
    8081 = 13*621 + 8; hence not 13 divides 8081 by NAT_4:9;
    8081 = 17*475 + 6; hence not 17 divides 8081 by NAT_4:9;
    8081 = 19*425 + 6; hence not 19 divides 8081 by NAT_4:9;
    8081 = 23*351 + 8; hence not 23 divides 8081 by NAT_4:9;
    8081 = 29*278 + 19; hence not 29 divides 8081 by NAT_4:9;
    8081 = 31*260 + 21; hence not 31 divides 8081 by NAT_4:9;
    8081 = 37*218 + 15; hence not 37 divides 8081 by NAT_4:9;
    8081 = 41*197 + 4; hence not 41 divides 8081 by NAT_4:9;
    8081 = 43*187 + 40; hence not 43 divides 8081 by NAT_4:9;
    8081 = 47*171 + 44; hence not 47 divides 8081 by NAT_4:9;
    8081 = 53*152 + 25; hence not 53 divides 8081 by NAT_4:9;
    8081 = 59*136 + 57; hence not 59 divides 8081 by NAT_4:9;
    8081 = 61*132 + 29; hence not 61 divides 8081 by NAT_4:9;
    8081 = 67*120 + 41; hence not 67 divides 8081 by NAT_4:9;
    8081 = 71*113 + 58; hence not 71 divides 8081 by NAT_4:9;
    8081 = 73*110 + 51; hence not 73 divides 8081 by NAT_4:9;
    8081 = 79*102 + 23; hence not 79 divides 8081 by NAT_4:9;
    8081 = 83*97 + 30; hence not 83 divides 8081 by NAT_4:9;
    8081 = 89*90 + 71; hence not 89 divides 8081 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8081 & n is prime
  holds not n divides 8081 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
