---
title: Prime Numbers
description: Prime numbers are integers greater than one divisible only by themselves and one. Learners will understand their distribution, factorization properties, and fundamental role in number theory and modern encryption algorithms.
category: mathematics
subcategory: number-theory
difficulty: beginner, intermediate, advanced
url: /subject/prime-numbers
---

# Prime Numbers

Prime numbers are integers greater than one divisible only by themselves and one. Learners will understand their distribution, factorization properties, and fundamental role in number theory and modern encryption algorithms.

## Available Resources

1 Videos • 1 Books • 1 Courses • 3 Websites

## Websites

### 1. OEIS Prime Sequences

Search results for prime-related entries in the On-Line Encyclopedia of Integer Sequences, the standard database for number sequences. Each entry gives terms, formulas, references and code, letting readers identify a sequence met in their own work and trace its literature.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://oeis.org/search?q=prime&language=english&go=Search

**Tags:** integer sequences, prime numbers, number theory, reference database

### 2. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

### 3. primes.utm.edu

Primes.utm.edu, The Prime Pages, is a comprehensive number theory resource focused on primes, offering extensive prime catalogs (including Mersenne primes), historical notes, tables, and references to algorithms, software, and research data.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://t5k.org/

**Tags:** websites, mathematics-statistics, mathematics

## Videos

### 1. But what is the Riemann zeta function? Visualizing analytic continuation

**Author:** Grant Sanderson

Animated 3Blue1Brown explanation of how the zeta function is defined for complex inputs and extended beyond its region of convergence by analytic continuation. Viewers come to understand what the Riemann hypothesis actually claims and why it connects to the primes.

**Difficulty:** Intermediate | **Price:** Free

**Link:** https://www.youtube.com/watch?v=sD0NjbwqlYw

**Tags:** riemann zeta function, analytic continuation, complex analysis, riemann hypothesis

## Courses

### 1. Number Theory

Four-week UC San Diego course building from division with remainder and modular arithmetic to Euclid's algorithm and RSA. Finishing it, you can encrypt and decrypt messages and break RSA implementations that reuse or mishandle keys.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://www.coursera.org/learn/number-theory-cryptography

**Tags:** courses, mathematics-statistics, mathematics

## Books

### 1. The Music of the Primes

**Author:** Marcus du Sautoy

Popular history of the Riemann hypothesis by an Oxford mathematician, following Gauss, Riemann, Hardy, Ramanujan and later researchers. Readers come away understanding, without formal mathematics, why prime distribution is tied to the zeta zeros and why it matters for cryptography.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/1841155799?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, number-theory

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