Sieve of Eratosthenes Generator (Free) – List Primes & Find the Nth Prime

Enter an upper bound to generate a list of primes with the Sieve of Eratosthenes, visualized step by step. Also look up the Nth prime (up to the 1,000,000th) — free, browser-based, no sign-up.

Sieve of Eratosthenes for 1–100 (Reference Table)

Green cells are prime numbers; the rest were eliminated by the sieve.

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

1 is neither prime nor composite, so it is left uncolored.

Tips

  • The Sieve of Eratosthenes efficiently lists all primes up to N by crossing out the multiples of each prime it finds, starting from 2.
  • Set the upper bound N to 400 or below to see exactly which prime eliminated which number, step by step.
  • The Nth-prime lookup supports queries like "what is the 1,000,000th prime," useful for confirming the existence of very large primes.
  • Everything runs locally in your browser — the generated prime list is never sent to a server.

FAQ

It is a primality-listing method credited to the 3rd-century-BCE mathematician Eratosthenes. Starting from 2, you mechanically cross out the multiples of each prime you find; whatever remains is prime. Because it only requires simple repeated operations, it is well suited to computer implementation.

Since all computation runs in your browser, the upper bound is capped at 1,000,000. Going beyond that would sharply increase the workload and could make the browser unresponsive.

The Prime Number Theorem gives an estimated upper bound for the Nth prime, and the sieve is run over that range to find it exactly. Lookups are supported up to the 1,000,000th prime.

When there are many results, only the first 1,000 are displayed, with the remaining count summarized. Step-by-step visualization is only available for upper bounds of 400 or below.
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Side Note — Why a 2,000-year-old algorithm is still in use

The Sieve of Eratosthenes is one of the oldest surviving prime-generating algorithms, credited to the ancient Greek scholar Eratosthenes, who served as chief librarian of the Library of Alexandria in the 3rd century BCE. That a method devised over two millennia ago is still taught in computer science courses today speaks to its elegant simplicity.

The mechanism is disarmingly simple: list the integers starting from 2, treat the smallest unmarked number as prime, and cross out all of its multiples. Repeat this up to √N, and every prime up to N is revealed. For generating a full list of primes, this is far more efficient than testing each number individually with trial division.

The search for enormous primes continues today — distributed-computing projects like GIMPS (the Great Internet Mersenne Prime Search) keep discovering Mersenne primes with tens of millions of digits. The sieve itself is not used to find primes that large, but its core idea — mechanically eliminating multiples — underlies more advanced primality-testing algorithms.

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