The Bunyakovsky conjecture is a conjecture in number theory that relates to prime numbers and is named after the Russian mathematician Viktor Bunyakovsky. It deals with the existence of prime numbers generated by certain polynomial expressions.

A balanced prime is a special type of prime number that is defined in relation to its neighboring prime numbers. Specifically, a prime number \( p \) is considered to be a balanced prime if it is the average of the nearest prime numbers that are less than and greater than \( p \).

The Thomson problem is a well-known problem in physics and mathematical optimization that involves determining the optimal arrangement of point charges on the surface of a sphere. Specifically, it seeks to find the configuration of \( N \) equal positive charges that minimizes the potential energy of the system due to their electrostatic repulsion.

Uses Redux, while reactjs/react-rails appears to do that more manually

Lots of focus on Heroku deployability, which is fantastic: shakacode.gitbooks.io/react-on-rails/content/docs/additional-reading/heroku-deployment.html

Live instance: www.reactrails.com/ with source at: github.com/shakacode/react-webpack-rails-tutorial Not the most advanced web-app (a gothinkster/realworld-level would be ideal). Also has clear dependency description, which is nice.

Trying at github.com/shakacode/react-webpack-rails-tutorial/tree/8e656f97d7a311bbe999ceceb9463b8479fef9e2 on Ubuntu 20.10. Got some failures: github.com/shakacode/react-webpack-rails-tutorial/issues/488 Finally got a version of it working at: github.com/shakacode/react-webpack-rails-tutorial/issues/488#issuecomment-812506821

Oh, and the guy behind that project lives in Hawaii (Ciro Santilli's ideal city to live in), has an Asian-mixed son, and two Kinesis Advantage 2 keyboards as seen at twitter.com/railsonmaui/status/1377515748910755851, Ciro Santilli was jealous of him.

Cramér's conjecture is a hypothesis in number theory related to the distribution of prime numbers. It was proposed by the Swedish mathematician Harald Cramér in 1936. The conjecture specifically addresses the gaps between consecutive prime numbers. Cramér's conjecture suggests that the gaps between successive primes \( p_n \) and \( p_{n+1} \) are relatively small compared to the size of the primes themselves.

A congruent number is a natural number that is the area of a right triangle with rational number side lengths. In other words, a positive integer \( n \) is called a congruent number if there exists a right triangle with legs of rational lengths such that the area of the triangle is equal to \( n \).

Artin's conjecture on primitive roots is a conjecture in number theory proposed by Emil Artin in 1927. It concerns the existence of primitive roots modulo primes and more generally, modulo any integer.

An M/G/k queue is a specific type of queueing model used in operations research and telecommunications to analyze systems where "customers" (or tasks or jobs) arrive, get serviced, and depart. The notation M/G/k provides insight into the characteristics of this queueing system: - **M**: Stands for "Markovian" or "memoryless" arrival process.

The Inverse Galois Problem is a central question in the field of algebra, particularly in the area of field theory and algebraic geometry. It seeks to determine whether every finite group can be represented as the Galois group of some field extension of the rational numbers \(\mathbb{Q}\) or more generally, of some base field.

The Erdős–Ulam problem is a question in the field of combinatorial geometry, named after mathematicians Paul Erdős and George Ulam. The problem relates to the arrangement of points in Euclidean space and how subsets of those points can be grouped to form convex sets.

Cousin primes are pairs of prime numbers that differ by four. In mathematical terms, if \( p \) and \( q \) are prime numbers and \( q = p + 4 \), then \( (p, q) \) is a cousin prime pair.

Integrations React integration:

The Grothendieck–Katz \( p \)-curvature conjecture is a conjecture in the field of algebraic geometry and number theory, particularly dealing with \( p \)-adic differential equations and their connections to the geometry of algebraic varieties. The conjecture is concerned with the behavior of differential equations over fields of characteristic \( p \), especially in relation to \( p \)-adic representations and the concept of \( p \)-curvature.

A **palindromic prime** is a number that meets two criteria: 1. **Palindromic**: It reads the same forwards and backwards. For example, 121, 131, and 1221 are palindromic numbers. 2. **Prime**: It is a prime number, meaning it has no positive divisors other than 1 and itself.

A Newman–Shanks–Williams (NSW) prime is a specific type of prime number that is related to a particular sequence known as the Newman–Shanks–Williams sequence.

The Second Neighborhood Problem is a concept in the field of graph theory and network analysis, particularly relevant in the study of social networks and community detection. It is often associated with the analysis of local structures within a network. In this context, the "first neighborhood" of a node refers to all directly connected nodes, meaning the immediate neighbors of that node. The "second neighborhood" extends this concept by considering the neighbors of those immediate neighbors.

The Brennan Conjecture is a mathematical conjecture related to the properties of certain kinds of graphs, specifically in the field of graph theory. It concerns the relationship between the diameter of a graph and the maximum degree of its vertices. The conjecture asserts that for any graph with a given maximum degree, there is a bound on the diameter that can be expressed in terms of that degree.

The Berman-Hartmanis conjecture is a hypothesis in computational complexity theory that relates to the structure of problems within the complexity classes P and NP. Formulated by Jacob Berman and Richard Hartmanis in the early 1970s, the conjecture posits that every NP-complete problem can be efficiently transformed into any other NP-complete problem in a way that preserves the number of solutions.

A conjecture is an educated guess or a proposition that is put forward based on limited evidence, which has not yet been proven or disproven. In mathematics and science, conjectures arise from observations or patterns that suggest a certain conclusion, but they need formal proof or experimental validation to be accepted as a theorem or law.

Harborth's conjecture is a hypothesis in the field of graph theory, particularly related to the properties of planar graphs. Specifically, it suggests that every planar graph can be colored using at most four colors such that no adjacent vertices share the same color. This assertion is closely related to the well-known Four Color Theorem, which states that four colors are sufficient to color the vertices of any planar graph.