Lecture

Number Theory: More Facts about Primes

Related lectures (30)

Covers the distribution of primes, arithmetic progressions, Mersene primes, and Goldbach's Conjecture.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Prime Numbers and Primality Testing

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Prime Number Theorem

Explores the proof of the Prime Number Theorem and its implications in number theory.

Number Theory: Primes

Covers the definition of primes, the Fundamental Theorem of Arithmetic, and Euclid's Theorem.

Primes: Fundamental Theorem and Sieve of Eratosthenes

Explores primes, the Fundamental Theorem of Arithmetic, trial division, the Sieve of Eratosthenes, and Euclid's Theorem.

Dirichlet Characters: Definition and Properties

Explores Dirichlet characters, covering their definition, periodicity, and properties through a mock exam.

The Riemann Hypothesis

Explores the Riemann Hypothesis, prime numbers, Zeta-function, and quantum mechanics.

Primes in arithmetic progressions (II), and Gamma functions

Explores the existence of primes in arithmetic progressions and the properties of the Euler gamma function.

Prime Number Theorem

Covers the proof of Von Mangoldt's formula and the Prime Number Theorem using Zeta functions and pole analysis.

Mertens' Theorems and Mobius Function

Explores Mertens' theorems on prime estimates and the behavior of the Mobius function in relation to the prime number theorem.

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Prime Numbers: Euclid's Theorem

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Number Theory: Fundamental Concepts

Covers binary addition, prime numbers, and the sieve of Eratosthenes in number theory.

Number Theory: History and Concepts

Explores the history and concepts of Number Theory, including divisibility and congruence relations.

Integers: Sets, Maps, and Principles

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Primes in Arithmetic Progression

Explores primes in arithmetic progression, focusing on L-functions, characters, and the divergence of the sum of 1 over p for p congruent to a modulo q.

Local Rings and Minimal Primes

Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.

Algebraic Structures: Groups and Rings

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Multicorrelation Sequences and Primes

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.