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 |
Prime Number Generator — List Primes in Any Range
Generate every prime between two numbers, or all primes up to any value up to 1,000,000. The same sieve that powers the checker above, run over the whole range at once.
168 primes between 1 and 1,000.
Frequently Asked Questions
Related Math Tools
Factor Calculator
All factors and prime factors of a number.
Rectangle Calculator
Area, perimeter and diagonal of rectangles.
Decimal to Fraction Calculator
Decimals to fractions, simplified.
Binary Converter
Binary, decimal, hex and two’s complement conversions.
Roman Numerals Converter
Numbers to Roman numerals and back.
Check Out Other Popular Tools
Noindex Checker
Check if your website is blocked from Google search results by robots.txt, noindex tags, or headers.
Page Size Checker
Instantly measure the HTML document size of any webpage to optimize load speed and SEO performance.
Russian Proficiency Test (TORFL)
Test your Russian level with our free adaptive 40-question TORFL assessment. Get an instant CEFR score mapped to official TRKI levels and a PDF certificate.
Was this tool helpful?
Comments
Loading comments...