Prime Factorization
Break any whole number into its prime factor building blocks.
A prime number generator lists all prime numbers up to a specified limit using the Sieve of Eratosthenes — an ancient algorithm that is still one of the most efficient methods.
- 1Start with all numbers from 2 to n as potentially prime
- 2Mark all multiples of 2 as composite
- 3Move to next unmarked number; mark its multiples
- 4Repeat until √n; remaining unmarked numbers are prime
Primes up to 30=2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (10 primes)
| Range | Primes | Density (% prime) |
|---|---|---|
| 1–100 | 25 | 25% |
| 1–1,000 | 168 | 16.8% |
| 1–10,000 | 1,229 | 12.3% |
| 1–100,000 | 9,592 | 9.6% |
| 1–1,000,000 | 78,498 | 7.8% |
References
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