Number Theory
Prime Number Theorem - Number Theory
Learn the prime number theorem with examples, step-by-step guide, and calculator tools. Approximate number of primes less than x
The prime number theorem is a fundamental concept in number theory. Approximate number of primes less than x. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[\pi(x) \approx \frac{x}{\ln x}\]
Variables
π(x)
Number of primes ≤ x
ln
Natural logarithm
Step-by-Step Guide
- 1
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 4
Step 4: Interpret the result
Examples
Example 1
Example 1: [] → π(100) ≈ 100/ln(100) ≈ 21.7 (actual: 25)
Example 2
Example 2: ≈ 21.7
Frequently Asked Questions
What is the prime number theorem?
Approximate number of primes less than x
How do I calculate prime number theorem?
Use the formula: \pi(x) \approx \frac{x}{\ln x}. Follow the steps provided above.
What tools can help with prime number theorem?
We provide online calculators: calculator