
theorem
  4159 is prime
proof
  now
    4159 = 2*2079 + 1; hence not 2 divides 4159 by NAT_4:9;
    4159 = 3*1386 + 1; hence not 3 divides 4159 by NAT_4:9;
    4159 = 5*831 + 4; hence not 5 divides 4159 by NAT_4:9;
    4159 = 7*594 + 1; hence not 7 divides 4159 by NAT_4:9;
    4159 = 11*378 + 1; hence not 11 divides 4159 by NAT_4:9;
    4159 = 13*319 + 12; hence not 13 divides 4159 by NAT_4:9;
    4159 = 17*244 + 11; hence not 17 divides 4159 by NAT_4:9;
    4159 = 19*218 + 17; hence not 19 divides 4159 by NAT_4:9;
    4159 = 23*180 + 19; hence not 23 divides 4159 by NAT_4:9;
    4159 = 29*143 + 12; hence not 29 divides 4159 by NAT_4:9;
    4159 = 31*134 + 5; hence not 31 divides 4159 by NAT_4:9;
    4159 = 37*112 + 15; hence not 37 divides 4159 by NAT_4:9;
    4159 = 41*101 + 18; hence not 41 divides 4159 by NAT_4:9;
    4159 = 43*96 + 31; hence not 43 divides 4159 by NAT_4:9;
    4159 = 47*88 + 23; hence not 47 divides 4159 by NAT_4:9;
    4159 = 53*78 + 25; hence not 53 divides 4159 by NAT_4:9;
    4159 = 59*70 + 29; hence not 59 divides 4159 by NAT_4:9;
    4159 = 61*68 + 11; hence not 61 divides 4159 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4159 & n is prime
  holds not n divides 4159 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
