Generate Random Prime Numbers

Prime numbers are the atoms of arithmetic, and random samples of them are surprisingly useful — as practice material for factorisation, as the raw ingredients of public-key cryptography, and as the punchline of countless puzzles. But you cannot just pick them by hand: primality is invisible until you check, and checking dozens of numbers by trial division is slow and miserable.

Generate Random Prime Numbers samples verified primes from any interval up to five million. Set a minimum and maximum, choose how many you want, and every value returned has been proven prime by a complete sieve of Eratosthenes — no repeats, no composites, no probabilistic guesswork. The output is ready to copy or download for worksheets, cryptography exercises and experiments.

• Any interval up to 5,000,000: Choose exactly where your primes come from — small ranges for teaching, large ones for data.
• Provably prime: Every result comes from a full sieve of Eratosthenes, not a probabilistic test.
• No duplicates: Samples without replacement, so a draw of 10 gives 10 different primes.
• Honest about small ranges: If the interval cannot satisfy your request, it tells you how many primes actually exist there.
• Live redraw: Change the interval or count and a fresh sample appears instantly.
• Copy or download: One number per line, ready for worksheets and scripts.
• Fast sieving: The interval is sieved once and samples are drawn from it in milliseconds.
• Free and private: Everything runs in your browser; nothing is uploaded.

1. Set the interval. Enter a minimum and maximum — for example 1 and 100 for everyday primes.
2. Choose how many primes you want. Up to 10,000 in one draw.
3. Hit Generate. The interval is sieved and the sample is drawn instantly.
4. Check the stats. The output notes how many primes exist in the whole interval, so you always know if your request was even possible.
5. Copy or download. Take the list elsewhere in one click.
6. Reroll when needed. Generate again for a completely different sample from the same interval.

Example 1 — Classroom factorisation drill. Draw 20 random primes between 100 and 1000. The result gives students a fresh set of numbers to factor or check, with no duplicates and no composites slipping through.

Example 2 — Cryptography practice. Generate 5 primes between 100,000 and 1,000,000 and run them through the primality-test tool to see the sieve in action at scale.

Example 3 — Number theory experiment. Sample 200 primes from the interval 1 to 100,000 and look at their gaps and endings — a quick, honest look at how primes distribute.

Example 4 — Puzzle construction. Building a puzzle where a hidden prime unlocks the answer? Draw a prime in a specific range so you know the solution exists before you build the puzzle around it.

• Verified, not guessed: Complete sieving proves every output prime.
• Exactly the interval you want: Narrow or wide, small or up to five million.
• Distinct results: Samples never repeat within a list.
• Instant feedback: Knows whether your request is possible and says so.
• Teaching and crypto ready: Suitable for worksheets, drills and key-generation practice.
• Free and private: Runs entirely in the browser with nothing uploaded.