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Prime Number Generator
Generate the first N prime numbers or list all primes inside a custom range. Includes prime count, largest prime, total sum, average prime gap, and twin-prime pair count for quick number-theory exploration.
Prime Number Generator
Use this free prime number generator to create the first N prime numbers or list all primes inside a custom numeric range. It is useful for classroom exercises, number theory exploration, programming tests, and mathematical pattern checks. The page also summarizes prime count, largest prime, total sum, average gap, and twin-prime pairs. Compare the result with the Random Number Generator, the Probability Calculator, the Factorial Calculator, or the wider Math & Statistics Calculators category.
Results
prime viewPrime count
50
First prime
2
Largest prime
229
Twin pairs
16
Prime Summary
Total Primes50
Prime Sum5,117
Average Gap4.63
Twin Prime Pairs16
Prime List
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229
What this prime number generator measures
This tool generates prime numbers and then summarizes the output with a few useful number-theory signals: how many primes appear, the first and last prime, the total sum, the average gap between neighboring primes, and how many twin-prime pairs appear in the result.
That makes it useful for education, algorithm testing, and quick mathematical exploration. If you want related numeric workflows, continue into the Probability Calculator, the Combinations Calculator, or the Mean Calculator.
How this calculator works
The generator uses a sieve approach, which starts by assuming numbers are prime and then marks multiples of each discovered prime as composite. The remaining unmarked values are prime numbers.
In first-N mode the tool estimates a safe upper bound, runs the sieve, and trims the output to the first requested primes. In range mode it runs the sieve up to the range end and filters the primes that fall inside your selected interval.
Worked examples
The default examples show two common workflows: generating the first 50 prime numbers and listing all primes between 100 and 500. Both are useful for checking prime density and learning how prime gaps change as numbers grow.
First 50 largest prime
229
100–500 prime count
70
100–500 twin pairs
16
In the range example, the result is not just a list of primes. It also gives you a quick summary of how frequently primes appear in that interval and how often they show up as twin-prime pairs.
Frequently asked questions
A prime number is a whole number greater than 1 that has exactly two positive divisors: 1 and itself. Examples include 2, 3, 5, 7, 11, and 13. Numbers like 4, 6, 8, and 9 are not prime because they can be divided evenly by additional integers.
Related tools
Use these related math tools to move from prime-number generation into combinatorics, probability, summary statistics, and broader number work.
Explore This Tool in Context
Prime Number Generator is part of the Math & Statistics Calculators collection. If you want a broader view of similar workflows, open the Math & Statistics Calculators category page or browse all QuickTools categories.
Common next steps after this tool include Ethereum ROI Calculator, Random Number Generator and Bitcoin ROI Calculator.
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