Composite Numbers Generator

Between the primes lie the composites: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18... every integer above 1 that has a divisor other than 1 and itself. Primes get all the attention, yet composites are the majority - more than 88 of every hundred integers, and their share only grows. Each one decomposes: 12 is 2 x 2 x 3, 15 is 3 x 5, 49 is 7 x 7 - and the smallest factor involved announces the composite immediately.

Composite Numbers Generator enumerates the composite list exactly, with one fast trial-division pass per run and the smallest prime factor for every term. Choose a start index and a count of up to 20,000 terms; every row shows rank, value and factor, and the whole run copies or downloads as index equals value lines.

• Exact enumeration: Candidates filtered by genuine primality trials - no sieve approximation, no skipped terms.
• Smallest prime factor: Every row carries the least prime that divides the value, a proof it is composite.
• Start anywhere: From composite number 1 to composite number 1,000,000, any run of up to 20,000 terms.
• Growing prime table: Detectors stay exact at any depth because the divisor list grows with the run.
• Copy or download: One click export of rank and value for the full run.
• Reference tab: The definition, the 1 and 0 caveats, the density story, the factorization link.
• Free and private: Everything runs locally - nothing is uploaded, stored or logged.

1. Set the start index - which composite to begin with (1 is 4, 2 is 6, and so on).
2. Set the count - consecutive composites to generate, up to 20,000.
3. Generate - candidates are tested against the growing prime table in one pass.
4. Read the factor - the smallest prime divisor on every row.
5. Copy or download the run for analysis, teaching or further work.

Example 1 - The opening run. Generate 12 terms from index 1: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21 - the first dozen integers that are neither prime nor 1.

Example 2 - Factor reading. Generate 20 terms and look at the factor column: evens all carry 2, 9 and 15 carry 3, 25 will carry 5 - the smallest divisor announces the pattern before the value does.

Example 3 - Squares. Start at index 13 to reach 25: the first square beyond the tenths, with 5 as its factor - every square is composite the moment its root is found.

Example 4 - A late stretch. Start at index 100,000, count 10: composite number 100,000 waits near 112,170 - a six-digit value, found in under a second by trial division.

Example 5 - Density check. Generate 1,000 terms and divide the last value by 1,000: roughly 1.16 composites exist per unit of the number line - the crowded world beyond the primes.

• Definition-true: Strictly the numbers with a proper divisor - never just the complement of a guessed prime list.
• Proof on every row: The smallest prime factor shows why each term belongs.
• Any depth: The millionth composite is reached by the same one-pass walk as the first.
• Educational: Pairs naturally with the prime generators to compare densities.
• Clean export: Rank and value lines ready for spreadsheets or homework.
• Private and free: All generation stays in the browser; nothing is uploaded or logged.