Question 1 comes up a lot. For example, it was discussed on <a href="https://groups.google.com/forum/?fromgroups=#!msg/sci.math/LWOtoA-w7XA/rPeoqgalh10J">sci.math</a> back in 1990. It was also discussed in print in the following article: > Quotients of primes, by David Hobby and D. M. Silberger, <i>Amer. Math Monthly</i> <b>100</b> (1993), 50–52. More recently it has shown up on <a href="http://answers.yahoo.com/question/index?qid=20081022093608AAZkzbJ">Yahoo Answers</a> and <a href="http://math.stackexchange.com/questions/4066/rationals-of-the-form-fracpq-where-p-q-are-primes-in-a-b">math.stackexchange.com</a>.