Chapter 9

Many of the computations in Chapter 9 are embedded in the .tex file.

The file num1check.sage runs several computations that take a little too long
for it to be practical to be put in the .tex file.

Run it with

sage num1check.sage

The output should read:

----------------
Sieving...
Preparing tables...
done.
Checking inequality for q<=30000r...
done.
Checking inequality for q>=30000r
Lemma 1.5: all tests passed.
Set of exceptions set([1, 2, 3, 5, 70, 39, 105, 10, 15, 195, 21, 165, 1365])
Persistent exceptions set([2, 5])
One last computation...

err_{1,R} is indeed >= - 0.001 for R>=48000
All tests passed.
----------------

The last computation takes longer than the previous ones taken together,
