Prime Number Checker – Is It Prime? Factors and Prime Lists
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Check if a number is prime, factorise it, or list all prime numbers between two values.
97 является простым числом
97 has exactly two divisors, 1 and itself.
Предыдущий прайм
89
Следующий прайм
101
Количество делителей
2
Оглавление
The prime number checker tells you instantly whether a number is prime, and if it is not, shows its prime factorisation and the smallest divisor that proves it. It also finds the previous and next prime, and can list every prime number in a range. For example, 97 is prime, while 91 is not, because 91 = 7 × 13.
How to use it
- Choose Is it prime? and enter a number up to one quadrillion (10^15), or
- choose List primes in a range and enter the start and end, such as 1 and 100.
What is a prime number?
A prime number is a whole number greater than 1 whose only divisors are 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Two is the only even prime. The number 1 is not prime, and every whole number above 1 is either prime or a product of primes in exactly one way, which is why factorisations are unique.
Prime numbers from 1 to 100
There are 25: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. There are 168 primes below 1,000 and 1,229 below 10,000.
How the check works
Small numbers are tested by division. Large numbers use the Miller–Rabin test with a fixed set of bases that is proven to give the right answer for every number in range, so a result of "prime" is certain, not a probability. Factorisation combines trial division with Pollard's rho method, which splits numbers made of two large primes quickly.
Related: GCD and LCM calculator and number to words.
Часто задаваемые вопросы
Is 1 a prime number?
No. A prime has exactly two divisors, 1 and itself. The number 1 has only one divisor, so it is neither prime nor composite.
How many prime numbers are there between 1 and 100?
There are 25 prime numbers between 1 and 100, from 2 to 97.
Is 2 a prime number?
Yes. 2 is the smallest prime and the only even one, because every other even number is divisible by 2.
How do you check if a large number is prime?
Test divisibility by primes up to its square root, or for very large numbers use the Miller–Rabin test, which this checker runs with bases that make the answer exact up to 10^15.
Is 91 a prime number?
No. 91 = 7 × 13.