Prime Number Finder
Find whether a given number is prime or discover all prime numbers within a specific range. Perfect for students, mathematicians, and cryptography enthusiasts.
Deterministic Prime Check (≤ 2⁶⁴ − 1)
Upper limit: 264 − 1 (18446744073709551615).
Enter a number above to check if it's prime
Find Primes in Range (Order-Agnostic)
Endpoints must be ≤ 264 − 1. Max width per query: 10000 numbers.
Enter a range above to find prime numbers
Applications of Prime Numbers
Prime Numbers are the most studied numbers in mathematics. Since they cannot be divided by any other number except themselves and 1, they have a lot of applications in the real world.
Cryptography
Prime numbers are the heart of modern encryption algorithms. RSA algorithm is considered one of the most secure encryption algorithms which is also based on prime numbers. Our whole encryption system relies upon the difficulty level of factoring the product of two large prime numbers. Bigger the number, greater the security.
Computer Science
Algorithms which can generate prime numbers at high speed and more efficiently consuming less amount of memory are always in demand. From generating random numbers to making hashing functions, prime numbers are always needed in various computer science applications.
Random Number Generation
Used in creating pseudo-random number generators
Hash Functions
Essential for creating efficient hash tables and checksums
Network Security
Foundation of secure communication protocols like HTTPS
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What are Prime Numbers?
Prime Numbers are those natural numbers which are greater than 1 and which cannot be represented in the form of multiplication of two digits. They are divided by 1 and themselves only. Prime Number is one of the most puzzling numbers in the mathematics field. Many scientists around the globe spent their decades of time in finding the nature of the prime numbers.
Examples:
2, 3, 5, 7, 11, 13, 17 etc are prime numbers since they are only divisible by 1 and themselves.
How to find if a number is a Prime Number?
Let us suppose a number N is given and we need to find if it is a prime or not. Since, proving a number is prime, is much harder than proving a number is not a prime.
Steps to check if a number is prime:
Check if N < 2
If the number N is less than 2, then it is not a prime number.
Check if N is even
If the number N is even and it is not 2, then it is not a prime number.
Check divisibility
Check if N is divisible by any odd number from 3 to √N. If divisible, then not prime.
Examples
Check if 23 is a prime number
Step 1: 23 is greater than 2. ✓
Step 2: 23 is not an even number. ✓
Step 3: From 3 to √23 ≈ 4.8, 23 is not divisible by 3. ✓
So, 23 is a prime number.
Check if 24 is a prime number
Step 1: 24 is not less than 2. ✓
Step 2: 24 is an even number. ✗
So, 24 is not a prime number.
Check if 15 is a prime number
Step 1: 15 is not less than 2. ✓
Step 2: 15 is not an even number. ✓
Step 3: Between 3 to √15 ≈ 3.9, 15 is divisible by 3. ✗
So, 15 is not a prime number (15 = 3 × 5).
Important Properties
Smallest Prime
2 is the smallest and only even prime number
Infinite Primes
There are infinitely many prime numbers (Euclid's theorem)
Twin Primes
Prime pairs with difference of 2 (e.g., 3,5 or 11,13)
Goldbach's Conjecture
Every even integer > 2 is sum of two primes