To directly answer your question: it is not generally possible to directly map each individual prime number to a specific pair of non-trivial zeros of the Riemann zeta function. The prime numbers themselves do not correspond to specific individual zeros of the zeta function in a direct, one-to-one manner.

Rather, the distribution of the prime numbers can be related to the distribution of the non-trivial zeros. The explicit formulas used in number theory show how the zeros of the zeta function influence the density and distribution of primes, but this relationship is more aggregate than specific.

There is a relationship between primes and the zeros of the Riemann zeta function, it is primarily about how the zeros collectively affect the distribution of primes, rather than establishing a direct, individual correspondence between each prime and a pair of non-trivial zeros.

The infinite sum of the Riemann zeta function is equal to an infinite product formula involving primes.

Thats about it thats well established.

Nothing to do with electrons please.

The evolutionary change of the physical parameters of the pendulum entails the dependence of its oscillation period on the evolutionary parameter $\tau$, therefore in the general case the function $T_{\sigma, t}(\tau)$ should be used as the oscillation period. However, in the case of $\sigma=\frac{1}{2}$ the trajectory of the pendulum evolves in accordance with the hyperbolic rotation $\psi = -\frac{1}{2}\log\tau$, and therefore the oscillation period is measured by the pseudo-Euclidean length of the full rotation of the pendulum and does not depend on the evolutionary parameter $\tau$. For example, the pseudo-Euclidean length of the closed trajectory of the $(1,1)$-torus knot of the pendulum corresponds to the period $T_{\frac{1}{2},0}$ , and the $n$-th part of the pseudo-Euclidean length of the trajectory of the $(1,n)$-torus knot of the pendulum corresponds to the period $T_{\frac{1}{2},t_{n}}$. And since the intersection points of the $(1,p)$-torus knot with the equator are uniformly distributed on the double shell of the sphere, it is possible that $s=\frac{1}{2} +\mathrm{i} t_{p}$ is a non-trivial root of the Riemann zeta function.