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Prime Number Calculator
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Enter a number
Prime Factorization
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Nearby Primes
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Prime Numbers Found
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Click generate to see primes
First 25 Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
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How to Use the Calculator
- Choose "Check if Prime" or "List Primes" mode
- For checking: enter any positive integer
- For listing: enter a range (e.g., 1 to 100)
- View results and prime factorizations
Prime Number Facts
- Infinite primes - Proven by Euclid ~300 BCE
- Cryptography - Large primes secure online transactions
- Fundamental theorem - Every integer > 1 has unique prime factorization
- Distribution - Primes become rarer but never stop
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Frequently Asked Questions
What is a prime number?
A prime number is a natural number greater than 1 that can only be divided evenly by 1 and itself. Examples: 2, 3, 5, 7, 11, 13...
Is 1 a prime number?
No, 1 is not considered a prime number. By definition, primes must be greater than 1 and have exactly two distinct factors.
Is 2 the only even prime?
Yes! 2 is the only even prime number. All other even numbers are divisible by 2, so they can't be prime.
What are twin primes?
Twin primes are pairs of primes that differ by 2, like (3,5), (11,13), (17,19). It's unknown if there are infinitely many twin primes.