The Prime Generator API provides lightning-fast access to a pre-computed database of prime numbers. Get any prime by its index position with sub-10ms response times. The database grows dynamically as more primes are computed.
Database-driven lookups with intelligent caching - 1-8ms response times
Clean JSON responses with just the index and prime number
Simple HTTP GET requests with JSON responses
Get the nth prime number (1-indexed) from our 10 billion prime database.
| Parameter | Type | Required | Description |
|---|---|---|---|
pi |
integer | Yes | Prime index (1 to current maximum). Use /stats endpoint to check current limit. Example: pi=1 returns 2 (first prime) |
GET https://vincentmossman.com/prime-generator/api?pi=100GET https://vincentmossman.com/prime-generator/api?pi=1000000GET https://vincentmossman.com/prime-generator/api?pi=1000000000
// 100th prime
{
"index": 100,
"prime": 541
}
// 1 millionth prime
{
"index": 1000000,
"prime": 15485863
}
// 1 billionth prime
{
"index": 1000000000,
"prime": 22801763489
}
| Field | Type | Description |
|---|---|---|
index |
integer | The requested prime index |
prime |
integer | The prime number at the given index |
Get current database statistics including maximum available prime index and build progress.
{
"database": {
"max_prime_index": 55000000,
"total_segments": 55,
"status": "in_progress",
"target_count": 10000000000
},
"cache": {
"cacheSize": 5,
"maxCacheSize": 100
},
"timestamp": "2025-08-05T15:30:45.123Z",
"version": "2025-08-05-dynamic"
}
{
"error": "Invalid prime index",
"message": "Index must be between 1 and 55,000,000",
"current_max": 55000000,
"requested": 100000000,
"suggestion": "Try a smaller index"
"example": "/prime-generator/api?pi=5"
}
{
"error": "Server busy - rate limit exceeded",
"message": "Too many requests. Please try again in 1 second.",
"limit": 5,
"window": "1 second",
"suggestion": "For bulk requests, add delays between calls"
}
{
"error": "Prime lookup failed",
"message": "Unable to retrieve the requested prime from database",
"index": 15000000000
}
Test the API directly from this page. Enter a prime index and see the live response.
// Get the 1 millionth prime
fetch('https://vincentmossman.com/prime-generator/api?pi=1000000')
.then(response => response.json())
.then(data => {
console.log(\`The ${data.index.toLocaleString()}th prime is: ${data.prime.toLocaleString()}\`);
// Output: "The 1,000,000th prime is: 15,485,863"
})
.catch(err => console.error('API Error:', err));
import requests
import time
# Test large prime lookup performance
start = time.time()
response = requests.get('https://vincentmossman.com/prime-generator/api?pi=500000000')
data = response.json()
end = time.time()
print(f"The {data['index']:,}th prime is: {data['prime']:,}")
print(f"Network + lookup time: {(end-start)*1000:.1f}ms")
# Typical output: "Network + lookup time: 45.2ms"
# Get a large prime quickly
curl "https://vincentmossman.com/prime-generator/api?pi=100000000" \
-H "Accept: application/json" \
-w "Response time: %{time_total}s\n"
# Batch multiple requests
for i in 1000000 10000000 100000000; do
echo "Prime #$i:"
curl -s "https://vincentmossman.com/prime-generator/api?pi=$i" | jq
done