
theorem
  3359 is prime
proof
  now
    3359 = 2*1679 + 1; hence not 2 divides 3359 by NAT_4:9;
    3359 = 3*1119 + 2; hence not 3 divides 3359 by NAT_4:9;
    3359 = 5*671 + 4; hence not 5 divides 3359 by NAT_4:9;
    3359 = 7*479 + 6; hence not 7 divides 3359 by NAT_4:9;
    3359 = 11*305 + 4; hence not 11 divides 3359 by NAT_4:9;
    3359 = 13*258 + 5; hence not 13 divides 3359 by NAT_4:9;
    3359 = 17*197 + 10; hence not 17 divides 3359 by NAT_4:9;
    3359 = 19*176 + 15; hence not 19 divides 3359 by NAT_4:9;
    3359 = 23*146 + 1; hence not 23 divides 3359 by NAT_4:9;
    3359 = 29*115 + 24; hence not 29 divides 3359 by NAT_4:9;
    3359 = 31*108 + 11; hence not 31 divides 3359 by NAT_4:9;
    3359 = 37*90 + 29; hence not 37 divides 3359 by NAT_4:9;
    3359 = 41*81 + 38; hence not 41 divides 3359 by NAT_4:9;
    3359 = 43*78 + 5; hence not 43 divides 3359 by NAT_4:9;
    3359 = 47*71 + 22; hence not 47 divides 3359 by NAT_4:9;
    3359 = 53*63 + 20; hence not 53 divides 3359 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3359 & n is prime
  holds not n divides 3359 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
