Prime Number Calculator
Check if a number is prime, find prime factors, and generate prime sequences
Maximum range: 10,000 numbers, end value up to 100,000
Maximum value: 10,000
Is Prime?
Prime Factorization
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Primes Found
prime numbers between and
The Prime Number
Step-by-Step Explanation
First 100 Prime Numbers
Prime Number Properties
Special Primes
- • 2 - Only even prime number
- • 3 - Smallest odd prime
- • 5 - Only prime ending in 5
- • Twin primes: (3,5), (5,7), (11,13), (17,19)...
Prime Milestones
- • 10th prime: 29
- • 100th prime: 541
- • 1000th prime: 7,919
- • Primes under 100: 25
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About Prime Number Calculator
What is a Prime Number Calculator?
A prime number calculator is a mathematical tool that helps you work with prime numbers in various ways. It can check if a number is prime, find the prime factorization of any integer, generate lists of prime numbers, and find the nth prime number.
How to Use This Calculator
- Prime Check Mode: Enter any number to instantly check if it's prime
- Prime Factorization Mode: Get the complete prime factorization of any integer
- Prime Generator Mode: Generate all prime numbers within a specified range
- Nth Prime Mode: Find the specific prime number at any position
Understanding Prime Numbers
What is a Prime Number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and the number itself.
Examples of Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37...
Composite Numbers
Numbers that have more than two factors are called composite numbers. Every composite number can be expressed as a unique product of prime numbers (Fundamental Theorem of Arithmetic).
Prime Number Properties
Key Facts
- 2 is the only even prime number
- 1 is neither prime nor composite
- All primes greater than 2 are odd
- There are infinitely many prime numbers (proven by Euclid)
- Prime numbers become less frequent as numbers get larger
Prime Density
The Prime Number Theorem states that the number of primes less than n is approximately n/ln(n). This means primes become "rarer" among larger numbers.
Primality Testing Methods
Trial Division
The simplest method: check if any number from 2 to √n divides n evenly. If none do, n is prime.
Sieve of Eratosthenes
An ancient algorithm that generates all primes up to a specified limit by iteratively marking the multiples of each prime.
Applications of Prime Numbers
- Cryptography: RSA encryption relies on the difficulty of factoring large primes
- Hash Functions: Prime numbers are used in hash table sizing
- Computer Science: Random number generation and data distribution
- Mathematics: Number theory, abstract algebra, and more
Frequently Asked Questions
Is 1 a prime number?
No, 1 is not considered a prime number. By modern definition, prime numbers must be greater than 1 and have exactly two distinct factors.
What is the largest known prime number?
As of 2024, the largest known prime is 2^82,589,933 − 1, a Mersenne prime with over 24 million digits.
How many prime numbers are there?
There are infinitely many prime numbers. Euclid proved this around 300 BCE with an elegant proof by contradiction.
Tip: Use this calculator to verify your manual calculations and explore the fascinating properties of prime numbers.