Matematika

Generátor prvočísel

Prime Factorization

Break any whole number into its prime factor building blocks.

Číslo

What is Prime Number Generator?

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Generátor prvočísel uvádí všechna prvočísla až do zadaného limitu pomocí Eratosthenova síta – starověkého algoritmu, který je stále jednou z nejúčinnějších metod.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

How to Prime Number Generator

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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

Worked Examples

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Example 1

Given:Primes up to 30

Výsledek:2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (10 primes)

Prime Density by Range

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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%

Frequently Asked Questions

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What is Prime Generator?

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. Use this calculator for accurate, instant results.

How accurate is the Prime Generator calculator?

The calculator uses the standard published formula for prime generator. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

What units does the Prime Generator calculator use?

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

What formula does the Prime Generator calculator use?

The calculator applies the standard formula for this type of calculation. See the 'How It Works' steps above for the detailed formula breakdown.

References

›Sieve of Eratosthenes — Wikipedia

Deep Dive

Read the full guide on how to use this calculator effectively

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Formula-verified for precision

Reviewed October 2026

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