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Check if a number is prime and analyze its mathematical properties
Enter a number to check if it's prime
17
97
24
49
31
29
The only even prime number
The largest prime less than 100
2^5 - 1, a Mersenne prime
p where 2p+1 is also prime
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 7 is prime because its only factors are 1 and 7.
Every composite number can be expressed as a unique product of prime numbers. For example, 12 = 2² × 3, where 2 and 3 are the prime factors.
We test divisibility up to the square root of the number. If no divisors are found, the number is prime. This is much more efficient than testing all numbers up to n.
Prime numbers are fundamental in cryptography, computer science, and mathematics. They're used in RSA encryption, hash functions, and random number generation.