
theorem
  8101 is prime
proof
  now
    8101 = 2*4050 + 1; hence not 2 divides 8101 by NAT_4:9;
    8101 = 3*2700 + 1; hence not 3 divides 8101 by NAT_4:9;
    8101 = 5*1620 + 1; hence not 5 divides 8101 by NAT_4:9;
    8101 = 7*1157 + 2; hence not 7 divides 8101 by NAT_4:9;
    8101 = 11*736 + 5; hence not 11 divides 8101 by NAT_4:9;
    8101 = 13*623 + 2; hence not 13 divides 8101 by NAT_4:9;
    8101 = 17*476 + 9; hence not 17 divides 8101 by NAT_4:9;
    8101 = 19*426 + 7; hence not 19 divides 8101 by NAT_4:9;
    8101 = 23*352 + 5; hence not 23 divides 8101 by NAT_4:9;
    8101 = 29*279 + 10; hence not 29 divides 8101 by NAT_4:9;
    8101 = 31*261 + 10; hence not 31 divides 8101 by NAT_4:9;
    8101 = 37*218 + 35; hence not 37 divides 8101 by NAT_4:9;
    8101 = 41*197 + 24; hence not 41 divides 8101 by NAT_4:9;
    8101 = 43*188 + 17; hence not 43 divides 8101 by NAT_4:9;
    8101 = 47*172 + 17; hence not 47 divides 8101 by NAT_4:9;
    8101 = 53*152 + 45; hence not 53 divides 8101 by NAT_4:9;
    8101 = 59*137 + 18; hence not 59 divides 8101 by NAT_4:9;
    8101 = 61*132 + 49; hence not 61 divides 8101 by NAT_4:9;
    8101 = 67*120 + 61; hence not 67 divides 8101 by NAT_4:9;
    8101 = 71*114 + 7; hence not 71 divides 8101 by NAT_4:9;
    8101 = 73*110 + 71; hence not 73 divides 8101 by NAT_4:9;
    8101 = 79*102 + 43; hence not 79 divides 8101 by NAT_4:9;
    8101 = 83*97 + 50; hence not 83 divides 8101 by NAT_4:9;
    8101 = 89*91 + 2; hence not 89 divides 8101 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8101 & n is prime
  holds not n divides 8101 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
