the prime number theorem (proof outline and additional notes)

Riemann's zeta function (links)

the Riemann Hypothesis (links)

p-adic numbers and adeles

D. Rockmore, "Chance in the Primes"

This excellent and thorough article is intended as a commentary to supplement the first half of a popular talk on the Riemann Hypothesis given by Peter Sarnak at a 1998 MSRI conference [a video recording is available here.]

how the complex zeros of Riemann's zeta function 'encode' the distribution of primes

the functional equation of the Riemann zeta function and related issues

D. Bump's lecture notes on the distribution of the Riemann zeta function's nontrivial zeros

R. Turco, M. Colonnese, M. Nardelli et al., "Sulle Spalle dei Giganti" (Italian language notes)

[authors' summary translation:] "This work presents various mathematical basic ideas, for the understanding of issues relating to the Riemann hypothesis (RH), the RH's equivalent and the GRH. This Block Notes of Math shows also subproblems of the RH, the LH hypotheses, the factorization and the main links between all the equations involved, through a grid connections.

The authors then show how the "RSA code" can be under attack, where the factorization of a semiprime N (N = a*b) is obtained through the Goldbach conjecture, with and a second-degree equation or through a second-degree equation of the type x² = a² mod N. Also they show how the problem of Basel has already solved in closed form for N odd with the constants zeta. Then they propose a new conjecture through the use of average cumulative Mertens function linked to the Mertens function and finally there is the presentation of a conjecture of how G(N), the number of solutions of Goldbach, and g(N), the number of twins primes, are linked with the logarithm integral of Gauss and the RH. This conjecture is candidate as additional and equivalent hypothesis of the RH."

summary of Ilan Vardi's (excellent) "Introduction to Analytic Number Theory"

quotations regarding the mystery of the prime distribution