Prime Numbers Studio
Discover the "atoms of mathematics". Use the Sieve of Eratosthenes to find primes, or verify any number instantly.
Sieve of Eratosthenes
This ancient algorithm finds prime numbers by filtering out the composite ones. Click Next Step to see how multiples (like 2, 4, 6...) get eliminated!
The Atoms of Mathematics
In Chemistry, everything is made of atoms. In Mathematics, every number is made of Prime Numbers. If a number isn't prime, it can be broken down into primes (e.g. 12 = 2 × 2 × 3). This makes primes the fundamental building blocks of the number universe.
The Sieve
Eratosthenes (276 BC) invented a clever way to find primes. Instead of checking divisors for each number, he simply walked through the list and eliminated multiples.
Secret Keepers
Primes are hard to find but easy to multiply. This "one-way" property is what protects your bank passwords and secure messages (RSA Encryption).
Deep Mystery
Mathematicians have been studying primes for 3000 years, but we still can't perfectly predict where the next one will appear. They are beautifully chaotic.
List of First 25 Primes
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
Frequently Asked Questions
What exactly is a Prime Number?
A prime number is a whole number greater than 1 whose only divisors are 1 and itself. Think of it as a number that cannot be broken into smaller integer pieces.
Why is 1 not a prime number?
For a number to be prime, it must have exactly TWO distinct factors (1 and itself). The number 1 only has ONE factor (1), so it fails the test.
What is the Sieve of Eratosthenes?
It is an ancient algorithm (over 2000 years old!) for finding all prime numbers up to a limit. It works by iteratively marking the multiples of each prime starting from 2. The numbers that remain unmarked are primes.
What is the only even prime number?
2 is the only even prime number. Every other even number (4, 6, 8...) is divisible by 2, which makes it composite.
Are there infinite prime numbers?
Yes! Euclid proved around 300 BC that there are infinitely many primes. No matter how high you count, you will always find another prime eventually.
What are Twin Primes?
Twin primes are pairs of prime numbers that differ by exactly 2. Examples include (3, 5), (5, 7), (11, 13), and (41, 43).
What are 'Mersenne Primes'?
Mersenne primes are primes that are one less than a power of two (2^n - 1). The largest known prime numbers are usually Mersenne primes.
How are prime numbers used in real life?
They are the backbone of internet security (RSA encryption). When you buy something online, your credit card data is protected using calculations involving massive prime numbers.
How do I check if a big number is prime?
For small numbers, check distinct factors up to its square root. for huge numbers, computers use randomized tests like the Miller-Rabin primality test.
What is the Pattern of Prime Numbers?
Primes appear randomly. There is no simple formula that generates all prime numbers, which is one of the biggest mysteries in mathematics (The Riemann Hypothesis).