Thousanddigit

Thousanddigit is a term used in mathematics and computer science to denote a numeric value consisting of exactly one thousand decimal digits. In this sense, a thousanddigit is any integer in the range from 10^999 to 10^1000 − 1. The concept is primarily used for illustrating properties of large integers, benchmarking arbitrary-precision arithmetic, and studying the performance of algorithms on large inputs.

Representation and storage: Thousanddigits are typically handled by arbitrary-precision arithmetic libraries that store the value as an array of limbs, such as 32- or 64-bit words, or as a digit array in a chosen base. The approximate binary size is about 3322 bits (log2(10) ≈ 3.3219 per decimal digit), which corresponds to roughly 415 bytes or about 104 32-bit words.

Generation and use: Thousanddigits can be produced randomly by concatenating 1000 decimal digits with a nonzero leading digit; they can also be generated deterministically from seeds for reproducible benchmarks. Applications include testing multiplication and division algorithms, primality testing on large integers, and evaluating the performance of arbitrary-precision libraries in non-cryptographic workloads.

Etymology and terminology: The term thousanddigit is a compound formed from thousand and digit; it is descriptive rather than a fixed mathematical term, and its usage varies by context. Related concepts include big integers and arbitrary-precision arithmetic.