NumberDB — The Number Database

The searchbar can be used to search for:

Real numbers:
Enter the number in one of three formats:
- Decimal representation including the period, e.g. "3.14" to search for pi. The search will be done in an interval around the entered number: Entering "3.14" will search for numbers in the interval (3.13, 3.15).
- Scientific notation (no period necessary), e.g. "14e2" to search numbers between 1300 and 1500.
- NumberDB's p-notation: Enter a term of the form "ApB", where A and B are integers. It corresponds to the number 10^A · 0.B, e.g. "1p314" for pi. The sign of the number is determined by the sign of B.
Fractional parts of real numbers:
Enter the first few digits after the period, e.g. "1415" for pi.
Integers:
Enter the exact integer without period, e.g. "-1". This works for integers with up to 127 binary digits (roughly 38 decimal digits). For longer integers, try to search them as real numbers.
Complex numbers:
Enter sums or differences of the form "A" or "i*A" or "A*i", where "A" is a real number in the above format or a rational number. Entering "-1/2 + i * 0.86602" (to search for a third root of unity) will search within a larger square around it. Both, real and imaginary parts need sufficient precision.
$p$-adic numbers:
Search for numbers in $\mathbb{Q}_p$ in one of two formats:
- Enter "Q2:1010" to search for $2^0 + 2^2 + O(2^4)$. Enter "Q2:1.1010" to search for $2^{-1} + 2^0 + 2^2 + O(2^4)$. For $p>10$, any $p$-adic digit needs to be given in base 10 with the same number of base 10 letters as $p$, e.g. "Q13:0102" will search for $13$-adic numbers of the form $1+2\cdot 13 + O(13^2)$. Minus signs are also interpreted, e.g. "Q3:-220" searches for $-(2 + 2\cdot 3^1) + O(3^3)$.
- Enter "3 + O(2^5)" or "2^0+2^1+O(2^5)" for numbers of the form $2^0 + 2^1 + O(2^5)$. This format also works for $\mathbb{Q}_p$, e.g. enter "3/5 + O(5^1)".
Polynomials over $\mathbb{Q}$:
Enter polynomials over $\mathbb{Q}$ in arbitrary variables, e.g. enter "x^6+y^6-x^5*y^5+4*x*y" to search for $x^6+y^6-x^5y^5+4xy$.
Tables:
Enter words from the table's title, keywords, tags, definition, or comments.
Tags:
Enter the first letters of one word of a tag, e.g. "irr" for the tag "Irrational".

Find the mathematics behind a number

NumberDB connects numerical values with the mathematical objects and formulas that produce them. Enter a number to look for matches, or search by a table title or mathematical topic. Search supports real, complex and p-adic numbers, as well as polynomials; advanced search lets you compare lists of values using SageMath expressions.

Explore 712 published tables or browse by mathematical subject. Tables describe their definitions, parameter conventions and references, with precision information and computational sources where available. Revision histories record how the data and explanations change.

Some places to start

NumberDB is collaborative and open source. You can suggest corrections or contribute a table through the website, API or Python package; contributions go through review. Learn how to use and contribute to NumberDB.