Ciro Santilli @cirosantilli  40

Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!

The private key is made of two randomly generated prime numbers: $p$ and $q$. How such large primes are found: how large primes are found for RSA.

The public key is made of:

Given a plaintext message m, the encrypted ciphertext version is:This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.

The inverse operation of finding the private m from the public c, e and $n$ is however believed to be a hard problem without knowing the factors of n.

However, if we know the private p and q, we can solve the problem. As follows.

First we calculate the modular multiplicative inverse. TODO continue.

Bibliography:

The second smallest non-Abelian finite simple group after the alternating group of degree 5.

Using green fluorescent protein as a protein tag.

The "Truth and Beauty" motto hugely coincides with Ciro Santilli's ideas.

Truth is easier somewhat as it is more subjective.

Beauty, like all arts, sometimes you achieve, sometimes you don't.

Searcing beauty is a painful thing. You just keep endlessly looking for that one new insight that will blow your mind.

The key missing point would be "usefulness". See also: Section "Art".

A way to write the wavefunction $\psi (x)$ such that the position operator is:i.e., a function that takes the wavefunction as input, and outputs another function:

If you believe that mathematicians took care of continuous spectrum for us and that everything just works, the most concrete and direct thing that this representation tells us is that:equals:

This operator case is surprisingly not necessarily mathematically trivial to describe formally because you often end up getting into the Dirac delta functions/continuous spectrum: as mentioned at: mathematical formulation of quantum mechanics

One dimension in position representation:

In three dimensions In position representation, we define it by using the gradient, and so we see that

Derived from classical first principles, matches Planck's law for low frequencies, but diverges at higher frequencies.