Prime Numbers In A Range Calculator

Work out prime numbers in a range instantly with clear inputs, formula shown and shareable results.

About Prime Numbers In A Range Calculator

Testing each candidate by trial division up to its square root finds all primes in a range. The prime number theorem predicts a density near 1/ln x, which the reported percentage can be compared against.

Formula

Prime density

π(x) ≈ x / ln x, so density near x is about 1 / ln x

Worked example

With the default values below, Prime Numbers In A Range Calculator returns Primes in the range of 21. Change any input above and every figure here is recalculated in your browser.

Inputs used

Fromminimum 1: 100
Tominimum 2: 200

Results

Primes in the range: 21
The primes: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
Sum of those primes: 3,167
Density of primes in the range: 20.7921 %

Step by step

1Values used
2Prime density
3Primes in the range= 21
4The primes= 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
5Sum of those primes= 3,167
6Density of primes in the range= 20.7921 %

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How many primes are between 100 and 200?

21, summing to 3167.

Do primes thin out?

Yes. There are 25 primes below 100 but only 21 between 100 and 200, and the density keeps falling like 1/ln x.