
theorem
  3559 is prime
proof
  now
    3559 = 2*1779 + 1; hence not 2 divides 3559 by NAT_4:9;
    3559 = 3*1186 + 1; hence not 3 divides 3559 by NAT_4:9;
    3559 = 5*711 + 4; hence not 5 divides 3559 by NAT_4:9;
    3559 = 7*508 + 3; hence not 7 divides 3559 by NAT_4:9;
    3559 = 11*323 + 6; hence not 11 divides 3559 by NAT_4:9;
    3559 = 13*273 + 10; hence not 13 divides 3559 by NAT_4:9;
    3559 = 17*209 + 6; hence not 17 divides 3559 by NAT_4:9;
    3559 = 19*187 + 6; hence not 19 divides 3559 by NAT_4:9;
    3559 = 23*154 + 17; hence not 23 divides 3559 by NAT_4:9;
    3559 = 29*122 + 21; hence not 29 divides 3559 by NAT_4:9;
    3559 = 31*114 + 25; hence not 31 divides 3559 by NAT_4:9;
    3559 = 37*96 + 7; hence not 37 divides 3559 by NAT_4:9;
    3559 = 41*86 + 33; hence not 41 divides 3559 by NAT_4:9;
    3559 = 43*82 + 33; hence not 43 divides 3559 by NAT_4:9;
    3559 = 47*75 + 34; hence not 47 divides 3559 by NAT_4:9;
    3559 = 53*67 + 8; hence not 53 divides 3559 by NAT_4:9;
    3559 = 59*60 + 19; hence not 59 divides 3559 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3559 & n is prime
  holds not n divides 3559 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
