Prime Number Checker
Check if any number is prime instantly. See complete factor breakdowns, step-by-step division tests, and prime lists.
Total Divisors
Factors of the number
Prime Factorization
Prime power representation
Neighboring Primes
Closest smaller & larger primes
All Factors (Divisors)
Step-by-Step Trial Division Proof
Rules for Prime Numbers
By definition in mathematics and number theory, a prime number is a positive whole number strictly greater than 1 that cannot be formed by multiplying two smaller natural numbers. It has exactly two distinct positive divisors: 1 and the number itself.
Use these five fundamental rules to quickly identify, test, or verify if any number is prime or composite:
1. Strictly Greater Than 1
Prime numbers must be integers strictly greater than 1 ($N > 1$). Neither 0 nor 1 are prime numbers. 1 is classified as neither prime nor composite because it has only one positive divisor (itself).
2. Exactly Two Positive Factors
A prime number can only be divided evenly by 1 and itself without leaving a remainder. If an integer has three or more divisors, it is classified as a composite number.
3. The Only Even Prime is 2
The number 2 is the smallest prime number and the only even prime number. Every other even number (4, 6, 8, 10...) is divisible by 2 and is therefore composite.
4. Square Root Limit (√N)
To check whether any integer N is prime, you only need to test prime divisors up to the square root of N (√N). If no prime divisor ≤ √N divides N evenly, N is guaranteed to be prime.
5. Ending Digit Rule for Large Primes
Every prime number greater than 5 must end with one of four digits: 1, 3, 7, or 9. Any multi-digit number ending in 0, 2, 4, 6, or 8 is even (divisible by 2), and any multi-digit number ending in 5 is divisible by 5.
List of Prime Numbers up to 100
There are exactly 25 prime numbers between 1 and 100. Click any prime below to load and verify it above.
| Number Range | Prime Numbers in Range | Count |
|---|---|---|
| 1 – 10 | 2, 3, 5, 7 | 4 |
| 11 – 20 | 11, 13, 17, 19 | 4 |
| 21 – 30 | 23, 29 | 2 |
| 31 – 40 | 31, 37 | 2 |
| 41 – 50 | 41, 43, 47 | 3 |
| 51 – 60 | 53, 59 | 2 |
| 61 – 70 | 61, 67 | 2 |
| 71 – 80 | 71, 73, 79 | 3 |
| 81 – 90 | 83, 89 | 2 |
| 91 – 100 | 97 | 1 |
| Total (1 – 100) | 25 Prime Numbers | 25 |
Frequently Asked Questions
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