Prime Integer Benchmark Calculator

Measure prime counting speed across custom integer ranges. Compare algorithms, samples, density, checks, and throughput. Download results for reliable integer benchmark records and reviews.

Calculator Input

Example Data Table

This table shows typical inputs and expected prime count behavior.

Start End Method Prime Count Use Case
1 100 Both 25 Quick correctness test
1 10,000 Sieve 1,229 Small range benchmark
100,000 200,000 Both 8,392 Algorithm comparison
1 1,000,000 Sieve 78,498 Larger workload timing

Formula Used

Prime Test Formula

Trial division checks whether an integer n has any divisor from 2 through √n. If no divisor exists, the integer is prime.

n is prime when n > 1 and n mod d ≠ 0 for every d ≤ √n.

Sieve Formula

The sieve marks multiples of each confirmed prime. Remaining unmarked values are prime. Its common time complexity is O(n log log n).

Density Estimate

The expected count uses the prime number theorem estimate. The rough formula is π(n) ≈ n / ln(n).

Benchmark Metrics

Average time equals total measured time divided by repetitions. Throughput equals tested integers divided by average seconds.

How to Use This Calculator

  1. Enter the starting integer for the benchmark range.
  2. Enter the ending integer. The page supports values up to 2,000,000.
  3. Select trial division, sieve, auto mode, or both methods.
  4. Choose warmup runs to reduce first-run timing noise.
  5. Set measured repetitions for a steadier average time.
  6. Choose how many primes should appear in the sample list.
  7. Press the calculate button to view results above the form.
  8. Use the CSV or PDF buttons to export the report.

Prime Integer Benchmark Guide

Why Prime Benchmarks Matter

Prime integer tests are useful for checking raw loop speed, memory behavior, and algorithm choice. They also give a simple way to compare changes in hosting, code, or server settings. This calculator turns a range of integers into a repeatable workload. It counts primes, measures time, and reports clear performance values.

Choosing the Right Method

Trial division is direct and easy to inspect. It tests each number against possible divisors. It works well for small ranges and teaching examples. The sieve method is usually faster for larger continuous ranges. It builds a table once and removes composite values quickly.

Understanding the Results

Prime count tells how many prime values exist inside your selected range. Density shows how common those primes are compared with all tested integers. The expected count uses a logarithmic estimate. It may not match exactly, especially for short ranges. That difference is normal.

Timing and Repeatability

A single run can be noisy. Other server tasks may affect timing. Warmup runs help reduce first-run effects. Repetitions make the average more useful. The minimum and maximum times show timing spread. Throughput converts the timing into integers tested each second.

Using Exports

CSV export is helpful for spreadsheets and audits. PDF export is better for sharing a compact report. The checksum helps confirm that repeated runs used the same prime set. Use the same range, method, and repetitions when comparing environments. This keeps your benchmark fair and easier to review.

Frequently Asked Questions

1. What does this benchmark calculate?

It counts prime integers inside a selected range. It also measures timing, density, gaps, twin pairs, throughput, and repeat stability.

2. Which method is faster?

The sieve is usually faster for larger continuous ranges. Trial division can be fine for small ranges or simple validation checks.

3. Why are warmup runs included?

Warmup runs reduce first-run noise. They are not included in the final timing average.

4. What is prime density?

Prime density is the prime count divided by total integers tested. It shows how common primes are in the chosen range.

5. Why is the expected count different?

The expected count uses a rough logarithmic estimate. Real prime counts vary, especially in smaller or narrow ranges.

6. What is the checksum for?

The checksum summarizes the discovered prime list. It helps confirm that repeated benchmark runs used matching results.

7. Can I export my results?

Yes. Use the CSV button for spreadsheet data. Use the PDF button for a compact benchmark report.

8. Why is the range capped?

The cap helps prevent long requests and memory issues on shared hosting. You can raise it after server testing.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.