
theorem
  4153 is prime
proof
  now
    4153 = 2*2076 + 1; hence not 2 divides 4153 by NAT_4:9;
    4153 = 3*1384 + 1; hence not 3 divides 4153 by NAT_4:9;
    4153 = 5*830 + 3; hence not 5 divides 4153 by NAT_4:9;
    4153 = 7*593 + 2; hence not 7 divides 4153 by NAT_4:9;
    4153 = 11*377 + 6; hence not 11 divides 4153 by NAT_4:9;
    4153 = 13*319 + 6; hence not 13 divides 4153 by NAT_4:9;
    4153 = 17*244 + 5; hence not 17 divides 4153 by NAT_4:9;
    4153 = 19*218 + 11; hence not 19 divides 4153 by NAT_4:9;
    4153 = 23*180 + 13; hence not 23 divides 4153 by NAT_4:9;
    4153 = 29*143 + 6; hence not 29 divides 4153 by NAT_4:9;
    4153 = 31*133 + 30; hence not 31 divides 4153 by NAT_4:9;
    4153 = 37*112 + 9; hence not 37 divides 4153 by NAT_4:9;
    4153 = 41*101 + 12; hence not 41 divides 4153 by NAT_4:9;
    4153 = 43*96 + 25; hence not 43 divides 4153 by NAT_4:9;
    4153 = 47*88 + 17; hence not 47 divides 4153 by NAT_4:9;
    4153 = 53*78 + 19; hence not 53 divides 4153 by NAT_4:9;
    4153 = 59*70 + 23; hence not 59 divides 4153 by NAT_4:9;
    4153 = 61*68 + 5; hence not 61 divides 4153 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4153 & n is prime
  holds not n divides 4153 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
