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First n prime numbers

List the first n prime numbers — the building blocks of arithmetic that have no divisors but 1 and themselves. Enter how many you want (up to 10,000) and it returns the sequence, the nth prime itself and the sum of them all.

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Enter How many primes (1–10000) and the First n prime numbers works out Prime numbers, The nth prime, Sum straight away. For instance, with How many primes (1–10000) = 100 it returns Prime numbers = 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, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, The nth prime = 541 and Sum = 24,133.

How to use it

  1. Enter your values: How many primes (1–10000).
  2. Read the result instantly: Prime numbers, The nth prime, Sum.

Frequently asked questions

How does the First n prime numbers work?

It takes How many primes (1–10000) and derives Prime numbers, The nth prime and Sum from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

A single value: How many primes (1–10000). Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With How many primes (1–10000) = 100, the calculator returns Prime numbers = 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, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, The nth prime = 541 and Sum = 24,133. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

How much does the result change with different inputs?

It moves a lot. Using How many primes (1–10000) = 200 instead, The nth prime goes from 541 to 1,223 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to How many primes (1–10000) = 50, The nth prime comes out at 229. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

What is the difference between the First n prime numbers and the List of prime numbers?

This one returns The nth prime; the List of prime numbers returns How many primes. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Twin prime finder is the closest one after this: Find every pair of twin primes up to a limit — primes that differ by exactly 2, like (11, 13) or (17, 19). Enter an upper bound (up to 1,000,000) and it lists the pairs and counts them. Whether infinitely many exist is one of the oldest open problems in mathematics.

What else is worth having open alongside it?

Prime factorization calculator and Prime number checker — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Find Prime Factors: Factor Trees and the Division MethodBreak any whole number into its prime building blocks with a factor tree or repeated division — and write the result as a clean prime factorization with exponents.ExplainerSignificant Figures Explained: Counting, Rounding, and Why They MatterLearn what counts as a significant figure, the rules for leading, trailing, and captive zeros, and how sig figs keep your calculated answers honest.How-toHow to Multiply and Divide Fractions: Multiply Across, Flip to DivideMultiplying fractions needs no common denominator — just multiply across. Dividing means multiplying by the reciprocal. Learn both with worked examples and how to simplify.How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.How-toHow to Add and Subtract Fractions: Common Denominator, Combine, SimplifyYou can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.How-toHow to Do Long Division: Divide, Multiply, Subtract, Bring DownLong division breaks a big division into a repeating four-step cycle. Learn the divide-multiply-subtract-bring-down loop and how to read the remainder, with a worked example.