Primes in Range API: Find All Primes Between Two Numbers

Need to find all prime numbers between 100 and 200? Or primes in any numeric range? The Primes in Range API uses optimized sieve algorithms to efficiently find every prime within your specified bounds.

Finding Primes in a Range

Finding all primes in a range is a common mathematical task. While you could check each number individually for primality, sieve-based algorithms are far more efficient for generating lists of primes.

For example, there are 21 primes between 100 and 200: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

Sieve Algorithms

The API uses efficient sieving techniques:

Sieve of Eratosthenes

Classic algorithm marking multiples of each prime as composite. Efficient for smaller ranges.

Segmented Sieve

Memory-efficient variant for large ranges, processing in segments.

Prime Counting

The API also provides pi(x) - the count of primes up to x - without listing them all.

Using the Primes in Range API

TinyFn provides an efficient endpoint to find primes in any range:

GET https://api.tinyfn.io/v1/math/primes-in-range?start=100&end=200
Headers: X-API-Key: your-api-key

{
  "start": 100,
  "end": 200,
  "primes": [101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199],
  "count": 21,
  "first_prime": 101,
  "last_prime": 199
}

Parameters

Code Examples

JavaScript / Node.js

const response = await fetch(
  'https://api.tinyfn.io/v1/math/primes-in-range?start=1&end=100',
  { headers: { 'X-API-Key': 'your-api-key' } }
);
const data = await response.json();
console.log(`Found ${data.count} primes between 1 and 100`);
console.log(`Primes: ${data.primes.join(', ')}`);

Python

import requests

response = requests.get(
    'https://api.tinyfn.io/v1/math/primes-in-range',
    headers={'X-API-Key': 'your-api-key'},
    params={'start': 1000, 'end': 2000}
)
data = response.json()
print(f"Primes between 1000-2000: {data['count']}")
print(f"First: {data['first_prime']}, Last: {data['last_prime']}")

cURL

curl "https://api.tinyfn.io/v1/math/primes-in-range?start=100&end=200" \
  -H "X-API-Key: your-api-key"

Common Use Cases

• Cryptography: Find primes of specific sizes for key generation
• Educational Tools: Visualize prime distribution
• Algorithm Testing: Generate prime test data
• Prime Gap Analysis: Study distances between consecutive primes
• Mathematical Research: Investigate prime patterns and conjectures

Best Practices

1. Use count_only for large ranges: When you need only the count, not the list
2. Set reasonable limits: Large ranges can return millions of primes
3. Page through results: For huge ranges, make multiple requests
4. Consider memory: Very large prime lists require significant memory
5. Cache common ranges: Primes do not change, so results can be cached