How Many Prime Numbers Are There Between 1 and 1000?
The concept of Prime Numbers From 1 to 1000 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding prime numbers helps students in quick calculations, mental maths, factorization, and cracking entrance exams like JEE, NTSE, and Olympiads.
What Is Prime Numbers From 1 to 1000?
A Prime Number is a natural number greater than 1 that has exactly two positive divisors: 1 and itself. Prime Numbers From 1 to 1000 are all the numbers in this range that satisfy this property. These numbers have a special significance in topics like prime factorization, co-prime numbers, HCF/LCM, and even cryptography. For example, 2, 3, 5, 7, and 11 are prime numbers because they can only be divided by 1 and themselves.
Key Formula for Prime Numbers From 1 to 1000
There is no direct algebraic formula to generate all prime numbers, but a prime number (p) must obey this rule: it is only divisible by 1 and p. Another important property is: if a number is not divisible by any prime less than or equal to its square root, then it is a prime.
List of Prime Numbers From 1 to 1000
Below is the complete, scrollable list of all prime numbers from 1 to 1000. This list is grouped for easy revision and quick lookup. There are 168 prime numbers in this range.
| Range | Prime Numbers | Count |
|---|---|---|
| 1–100 | 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 | 25 |
| 101–200 | 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 | 21 |
| 201–300 | 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 | 16 |
| 301–400 | 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397 | 16 |
| 401–500 | 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499 | 17 |
| 501–600 | 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599 | 14 |
| 601–700 | 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691 | 16 |
| 701–800 | 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797 | 14 |
| 801–900 | 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 | 15 |
| 901–1000 | 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 | 14 |
Total number of prime numbers from 1 to 1000 = 168.
How to Check if a Number is Prime?
You can check whether a number (like 337 or 997) is a prime number by:
- Checking divisibility by all prime numbers less than or equal to its square root.
- If it’s not divisible by any of these, it is a prime.
Example: Is 337 a prime number?
- Find the square root of 337 (approx. 18.3).
- Check divisibility by 2, 3, 5, 7, 11, 13, and 17.
- 337 is not divisible by any of them; so, 337 is prime.
Sieve of Eratosthenes: Write the numbers 1 to 1000 and systematically cross out all multiples of each prime, starting from 2. The numbers left uncrossed are the primes.
Properties and Applications of Prime Numbers From 1 to 1000
- There are infinitely many primes (proved by Euclid).
- 2 is the only even prime number.
- Every number greater than 1 can be represented as a product of prime numbers (Fundamental Theorem of Arithmetic).
- Primes play a vital role in computer encryption and secure data transfer.
- Prime numbers are often used in factorization questions in exams.
Step-by-Step Illustration
Find all prime numbers between 90 and 100.
1. List numbers: 91, 92, 93, 94, 95, 96, 97, 98, 99, 1002. Check which have only two divisors.
3. 97 is only divisible by 1 and 97.
Answer: 97 is the only prime in this range.
Speed Trick or Vedic Shortcut
A quick trick to check small numbers for primality: For numbers less than 100, check divisibility by 2, 3, 5, and 7. If not divisible, the number is likely prime. For larger numbers, use divisibility up to the square root.
In exams, memorize small primes to save time and use the grouping blocks in the table above for mental checklists. Vedantu’s math teachers share similar smart strategies in live concept sessions.
Try These Yourself
- Write the first five prime numbers from 1–20.
- Is 49 a prime number?
- List all prime numbers between 70 and 100.
- Identify all non-prime numbers between 10 and 20.
Frequent Errors and Misunderstandings
- Assuming 1 is a prime (it is not).
- Believing all odd numbers are prime.
- Missing 2 as the only even prime.
- Confusing co-prime with prime numbers.
Relation to Other Concepts
The idea of Prime Numbers From 1 to 1000 connects closely with Prime Factorization, co-primes, composite numbers, and factors & multiples. Mastering this helps with understanding more advanced math concepts and problem solving.
Classroom Tip
A simple way to remember: except for 2, all prime numbers are odd. Pair the learning with visual tables or color-coded charts for each group of 50 or 100, making mobile revision much easier. Vedantu’s faculty encourage such patterns for faster mastery!
We explored Prime Numbers From 1 to 1000—from definition, list, properties, and applications to step-by-step methods and quick checks. Keep practicing with Vedantu and use the links below to explore related topics for more confidence!
Continue Learning:
FAQs on Prime Numbers from 1 to 1000: Definition, List, and Tricks
1. What are prime numbers?
Prime numbers are whole numbers greater than 1 that are only divisible by 1 and themselves. They are the fundamental building blocks of all other whole numbers. Examples include 2, 3, 5, 7, and 11.
2. How many prime numbers are there between 1 and 1000?
There are 168 prime numbers between 1 and 1000.
3. What is the largest prime number less than 1000?
The largest prime number less than 1000 is 997.
4. Is 337 a prime number?
Yes, 337 is a prime number. Its only divisors are 1 and 337.
5. How can I quickly check if a number is prime?
To check if a number is prime, you can try dividing it by all prime numbers less than its square root. If none of these prime numbers divide evenly, then the number is prime. For example, to test if 337 is prime, divide it by primes like 2, 3, 5, 7, 11, 13, 17, and 19; if none are factors, 337 is prime.
6. What are some real-world applications of prime numbers?
Prime numbers are crucial in cryptography, particularly in securing online communications and transactions. They are also used in various areas of mathematics and computer science, including hashing algorithms and generating random numbers.
7. What is the difference between prime and composite numbers?
A prime number has only two factors (1 and itself), while a composite number has more than two factors. For example, 7 is prime (factors 1 and 7), but 9 is composite (factors 1, 3, and 9).
8. What is the Sieve of Eratosthenes?
The Sieve of Eratosthenes is an ancient algorithm used to find all prime numbers up to any given limit. It works by iteratively marking the multiples of each prime number, leaving only the primes unmarked.
9. Why isn't 1 considered a prime number?
The definition of a prime number requires it to have exactly two distinct positive divisors. The number 1 only has one divisor (itself), so it doesn't meet this criterion.
10. Are all odd numbers prime?
No. While many odd numbers are prime, some are composite. For example, 9 is an odd number but not a prime number because it is divisible by 3.
11. What are twin primes?
Twin primes are pairs of prime numbers that differ by 2. For example, 3 and 5, 5 and 7, 11 and 13 are twin primes.
12. What are co-prime numbers?
Two numbers are co-prime (or relatively prime) if their greatest common divisor (GCD) is 1. This means they share no common factors other than 1. For example, 15 and 22 are co-prime (GCD = 1), even though neither is a prime number.
