MathLivePrime number theorem
The prime number theorem states that the number of primes up to x is asymptotically x divided by the natural logarithm of x. It describes how primes thin out among the integers and is used in analytic number theory.
\lim_{x\to\infty}\frac{\pi(x)}{x/\ln(x)}=1What the symbols mean
| a large positive real number | |
| the prime-counting function, the number of primes less than or equal to x | |
| the natural logarithm of x |
About this formula
- FieldMathematics
- TopicNumber theory
- LevelUniversity
- Also calledprime counting function asymptotic, pi(x) approximation, distribution of primes, pi(x) ~ x/log x, Hadamard and de la Vallée Poussin theorem, prime number density
- SourceWikidata Q386292
Write it in Obsidian
MathLive is a free visual math editor for Obsidian. Run Find a formula, type “prime number theorem”, and it goes into your note as editable LaTeX. You can also scan formulas from screenshots, PDFs and handwriting.