Some questions about prime number research

Question

I'm an undergraduate who is studying for determination of prime number with my academic advisor. Before I meet her, I want to prepare more hardly. So, I'd like to ask you some questions that I'm most curious about.

1. In number theory sense, are the terminologies 'primorial' and 'primality' used? (primorial is the product prime numbers $p_1 p_2 \cdots p_n$ where $p_i$ is the $i-$th prime number.)

If I can use the terminology primality, my study is about the condition when given integer is prime number. I'm reading some books:

[1] G.H. Hardy and E.M. Wright, An introduction to the theory of numbers, 6th edn., Oxford University Press, 2008.

[2] J.V. Uspensky and M.A. Heaslet, Elementary Number Theory, New York: McGraw Hill, 1939.

[3] W. Narkiewicz, The Development of Prime Number Theory, New York: Springer-Verlag, 2000.

2. About reference, I could only find papers in computer science. But I want to read the papers in number theory. How can I find? Or, is there any recommended paper or book?

Thanks.

Answer 1

Question 1: Yes, primorial is used, see wikipedia. And also yes, primality is used, but prime element or prime number is used more often, see wikipedia.

Question 2: The literature given is excellent and not from computer science. To search for papers makes more sense when you have a more specific topic, e.g., the prime number theorem, or the Riemann hypothesis and so on.

Question 3: "How can I find it?" You can always search yourself with key words. I obtain $ 28 600 000$ search hits for "Prime Number Theorem". Usually the first $10$ hits are already quite helpful.