largenumber

Large numbers are integers whose magnitude is considered very large relative to ordinary counts. There is no universal threshold that defines a large number; what counts as large depends on context, such as everyday counting, scientific measurement, or abstract mathematics.

For representation, large numbers are usually written in decimal notation or in scientific notation, the latter expressing numbers as a × 10^b with 1 ≤ a < 10 and b an integer. Scientific notation is used to simplify comparison and calculation with numbers that would otherwise have many digits. Naming large numbers varies by region: the short scale and long scale assign different powers of ten to familiar terms like million, billion, and trillion, which can cause confusion in international texts, so many writers prefer explicit powers of ten.

Prominent examples include 10^6 (one million), 10^9 (one billion in the short scale), and 10^100 (googol). The term googolplex denotes 10^(10^100).

In mathematics, large numbers arise in combinatorics, probability, and number theory, where counts can explode with few elements. In computing, big-integer or arbitrary-precision libraries allow exact arithmetic on integers with hundreds or trillions of digits. In cryptography, large primes and large key sizes are used to secure digital communications.

Because growth is rapid, researchers often focus on asymptotic behavior and upper bounds rather than explicit values, studying how quantities scale with input size or parameters.