A circular prime is a particular type of prime number that remains prime when its digits are rotated in all possible ways. For example, let's consider the prime number 197. Its digit rotations are 197, 971, and 719, and since all of these numbers are prime, 197 is classified as a circular prime. To give another example, the number 13 is a circular prime because its rotations (13 and 31) are both prime numbers.

The Brumer bound is a concept from number theory, specifically in the study of algebraic number fields and their units. In the context of Class Field Theory and the study of the structure of units in the ring of integers of a number field, the Brumer bound provides a way to estimate the size of units in the ring of integers of an algebraic number field. More formally, it is a bound on the regulator of the unit group of the field's integers.

The term "broken diagonal" can refer to different concepts depending on the context. Here are a few possible meanings: 1. **Mathematics or Geometry**: In geometry, a broken diagonal may refer to a piecewise linear path in a grid or a geometric figure that consists of segments forming a diagonal-like shape but is not a straight line. For instance, in a geometric grid, a broken diagonal could zigzag from one corner of a rectangle to the opposite corner.

Brocard's conjecture is a hypothesis in number theory proposed by the mathematician Henri Brocard in 1876. It suggests that there are only a finite number of natural numbers \( n \) such that the expression \( n! + 1 \) (the factorial of \( n \) plus one) is a perfect square. In mathematical terms, Brocard's conjecture can be stated as: There are only finitely many integers \( n \) such that: \[ n!

The Brauer–Siegel theorem is a result in number theory concerning the behavior of the class numbers of number fields and their corresponding zeta functions. It specifically addresses the relationship between the growth of the class numbers of number fields and their degrees of extensions over the rational numbers.

Bonse's inequality is a mathematical result related to number theory, particularly in the context of prime numbers. Specifically, it provides a bound on the distribution of prime numbers and related sequences. The inequality asserts that for every positive integer \( n \), the sum of the reciprocals of the prime numbers up to \( n \) diverges logarithmically.

Bauerian extension is a concept in the field of functional analysis and related areas of mathematics, particularly concerning the extension of linear operators or functionals from one space to another. It is named after the mathematician Friedrich Bauer. In a more specific context, consider the problem of extending bounded linear functionals defined on a subspace of a Banach space to the entire space.

Arithmetic varieties, in the context of algebraic geometry, refer to varieties defined over number fields or more general arithmetic fields, and they can be studied using both algebraic techniques and number theoretic methods. These varieties are often associated with Diophantine equations, which seek integer or rational solutions to polynomial equations. More formally, an arithmetic variety is an algebraic variety defined over the field of rational numbers \( \mathbb{Q} \) or over more general number fields.

The Ankeny–Artin–Chowla congruence is a result in number theory concerning prime numbers and their distributions. Specifically, it deals with the congruence relationship of prime numbers in the context of quadratic residues. The conjecture can be stated as follows: For any odd prime \( p \) and any integer \( a \) that is relatively prime to \( p \), there exists a prime \( q \equiv a \pmod{p} \).

The Adleman–Pomerance–Rumely (APR) primality test is a deterministic algorithm for determining whether a given number is prime. It was developed by Leonard Adleman, Carl Pomerance, and Michael Rumely and is notable for its efficiency and robust theoretical foundation.

Élisabeth Lutz is a French diplomat known for her work in various capacities, including her role within the French Ministry of Foreign Affairs. Her career has involved international relations and diplomatic efforts, although specific details about her accomplishments and positions may not be widely publicized.

Édouard Lucas (1842–1891) was a French mathematician known for his work in number theory, particularly in the fields of prime numbers and combinatorial mathematics. He is perhaps best remembered for the Lucas sequence, a sequence of numbers that is similar to the Fibonacci sequence and defined by a recursive relation. Lucas also made significant contributions to the study of prime numbers, including Lucas primes and Lucas' theorem, which relates to binomial coefficients and modular arithmetic.

Zhiwei Yun can refer to various subjects depending on the context, including individuals, organizations, or concepts. However, without specific context, it's difficult to determine which Zhiwei Yun you are asking about.

Zeev Rudnick is likely a name that might reference a specific individual, possibly in academia or another field. However, without additional context, it is difficult to determine who exactly Zeev Rudnick is or what accomplishments or contributions they may have made. If you're referring to a specific person, could you please provide more context or detail?

Yutaka Taniyama was a Japanese mathematician known for his work in number theory and algebraic geometry. He is particularly famous for the Taniyama-Shimura-Weil conjecture, which posits a deep relationship between elliptic curves and modular forms. This conjecture was a central part of the proof of Fermat's Last Theorem by Andrew Wiles in the 1990s.

Yuri Linnik may refer to a specific individual, but without additional context, it's difficult to determine precisely which Yuri Linnik you are inquiring about. There are a few notable individuals with that name, including mathematicians or researchers in various scientific fields.

YoungJu Choie is not a widely recognized term or name in popular culture or notable references as of my last update in October 2023. It might refer to an individual, possibly in academia, arts, or another field. Without additional context, it's difficult to provide specific information about what or who YoungJu Choie is.

Yitang Zhang is a Chinese-American mathematician known for his work in number theory, particularly in relation to the distribution of prime numbers. He gained significant attention in 2013 for proving a major result regarding the existence of bounded gaps between prime numbers. Specifically, he showed that there are infinitely many pairs of prime numbers that differ by a bounded amount, a breakthrough in the field of additive number theory.

Yasutaka Ihara is a Japanese professional football (soccer) player known for playing as a defender. He has gained attention in both domestic and international leagues. Generally, players like Ihara are recognized for their skills on the pitch, contributions to their teams, and potential for career development.