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. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, etc. The number 1 is not considered prime, and 2 is the only even prime number.

How does the Sieve of Eratosthenes work?

The Sieve of Eratosthenes works by iteratively marking the multiples of each prime number starting from 2. It creates a list of numbers up to the desired limit, then systematically eliminates composite numbers (non-primes), leaving only the prime numbers.

What's the largest range I can search?

Our tool can search for prime numbers up to 1,000,000 (1 million) for performance reasons. For larger ranges, the algorithm becomes computationally expensive. If you need primes in larger ranges, consider using specialized mathematical software.

Why is 2 the only even prime number?

2 is the only even prime number because all other even numbers greater than 2 are divisible by 2, making them composite numbers. While 2 is even, it has no positive divisors other than 1 and itself.

What is prime density?

Prime density refers to the probability that a randomly selected number is prime. It decreases as numbers get larger, following approximately the function 1/ln(n), where n is the number. This means primes become increasingly rare as you go to higher numbers.

Can I use this for cryptography research?

Yes! Prime numbers are fundamental to modern cryptography, especially public-key cryptosystems like RSA. This tool can help you understand prime distribution and generate small prime numbers for educational purposes. However, for actual cryptographic use, much larger primes are required.

Prime Number Generator

Generate prime numbers within specified ranges using efficient algorithms for mathematical analysis and cryptographic applications. Perfect for number theory research, encryption key generation, and educational mathematics.

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Prime Number Settings

Configure the range for prime number generation

Minimum Range

Maximum Range

How it works: Uses the Sieve of Eratosthenes algorithm to efficiently find all prime numbers within your specified range. Perfect for mathematical analysis, cryptography education, and number theory.

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