The Number Dictionary
A comprehensive mathematical reference for number properties and classifications
Mission Statement
The Number Dictionary provides a systematic approach to number theory, offering detailed analysis and classification of integer properties. Established in 2008, this resource serves researchers, educators, and students seeking authoritative information on mathematical number properties.
Our platform implements rigorous computational algorithms to determine prime numbers, factorizations, and various number classifications, ensuring accuracy and reliability in mathematical analysis.
Computational Capabilities
Interestingness
Score and rank numbers by how many properties they have; top 1000 list and how the score is calculated
Number Systems
Numeral system representations: Sanskrit, Arabic, Roman, Maya, Chinese, Hebrew, Greek, Egyptian, Morse, duodecimal, vigesimal
Geometric Numbers
Multi-polygonal number sequences (triangular, square, pentagonal, hexagonal, etc.)
Perfect Powers
Determination of exponential representations and power decompositions
Abundant and Deficient Numbers
Classification based on sum of proper divisors relative to the number itself
Twin Prime Detection
Identification of prime pairs with difference of two
Negabinary Representation
Conversion to negative base numeral systems
Harshad Numbers
Numbers divisible by the sum of their digits
Kaprekar Numbers
Numbers whose square can be split into parts that sum to the original number
Smith Numbers
Composite numbers where the sum of digits equals the sum of prime factor digits
Sophie Germain & Safe Primes
Prime categories: Sophie Germain, safe prime
Fermat Numbers
Numbers of the form 2^(2^n)+1 (3, 5, 17, 257, 65537)
Refactorable number
Divisible by the count of its divisors (tau number)
Powerful number
Every prime factor has exponent ≥ 2
Hoax number
Composite: sum of digits = sum of digits of distinct prime factors
Technical Specifications
The Number Dictionary employs optimized algorithms for prime number computation, factorization, and number property determination. The system is designed for accuracy and computational efficiency, supporting analysis of integers up to specified maximum bounds.
Continuous development ensures the platform remains current with mathematical research and computational best practices. Regular updates enhance algorithmic performance and expand classification capabilities.
Developed and maintained by 
- Custom web applications and digital solutions
Version 1.9.0