When I am testing conjectures I have about number fields, I usually want to control the ramification, especially minimize to a single prime with tame ramification. Hence, I usually look for fields of prime discriminant (sometimes positive, sometimes negative).


I get the feeling that I cannot be the only one who does this...


And so, are there families of number fields of prime discriminant for each degree? Or at least degree 3 and 4? (They are the coolest. Except quadratics. Of course.) What about: given a prime - can I find a polynomial of degree d with the prime as its discriminant?



Families of number fields of prime discriminant
[Klueners Malle online](http://www.math.uni-duesseldorf.de/~klueners/groups2.html) might be just the thing you're looking for. Make your own lists! And [here](http://www.math.uni-duesseldorf.de/~klueners/minimum/minimum.html)'s some they made themselves, if you run out of ideas.


