Prime Number Checker

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are prime numbers because they cannot be divided evenly by any other numbers except 1 and themselves.

No, 1 is not considered a prime number. By definition, a prime number must have exactly two distinct positive divisors: 1 and itself. Since 1 only has one divisor (itself), it does not meet the criteria for being prime.

2 is the smallest prime number. It is also the only even prime number, as all other even numbers are divisible by 2 and therefore composite.

The prime checker uses an efficient algorithm that tests if a number is divisible by any integer from 2 up to the square root of the number. If no divisors are found, the number is prime. For range generation, it uses the Sieve of Eratosthenes algorithm for optimal performance.

You can check any number up to JavaScript's maximum safe integer (9,007,199,254,740,991). However, very large numbers may take longer to compute. For range generation, the maximum range span is limited to 1,000,000 numbers to ensure fast performance.

Composite numbers are positive integers greater than 1 that are not prime. They have at least one positive divisor other than 1 and themselves. For example, 4, 6, 8, 9, and 10 are composite numbers. The tool shows all factors for composite numbers.

Yes! Switch to "Generate Range" mode and enter your desired start and end values. The tool will generate a complete list of all prime numbers within that range, along with the total count. You can generate primes for any range up to 1,000,000 numbers.

The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to a specified integer. It works by iteratively marking the multiples of each prime as composite. This tool uses this efficient algorithm when generating prime numbers in a range.

Prime numbers are fundamental in mathematics and have practical applications in cryptography, computer science, and data security. RSA encryption, which secures internet communications, relies on the difficulty of factoring large numbers into their prime factors.

Yes, there are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid around 300 BCE. Despite being infinite, prime numbers become less frequent as numbers get larger.

Twin primes are pairs of prime numbers that differ by 2. For example, (3, 5), (5, 7), (11, 13), and (17, 19) are twin primes. The twin prime conjecture states that there are infinitely many twin primes, but this has not been proven.

The prime number checker is 100% accurate for all numbers within JavaScript's safe integer range. It uses mathematically proven algorithms for primality testing and the Sieve of Eratosthenes for range generation, ensuring complete accuracy.

Absolutely! This tool is perfect for learning about prime numbers, number theory, and mathematics. Students can experiment with different numbers, explore prime patterns, and understand the concept of primality through hands-on interaction.

Yes! When you check a composite (non-prime) number, the tool displays all of its factors (divisors), explaining why the number is not prime. This helps you understand the factorization of the number and learn about its mathematical properties.