An equidigital number is a number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. For example, in base-10 arithmetic 1, 2, 3, 5, 7, and 10 (2×5) are equidigital numbers. All prime number

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

s are equidigital numbers in any base.

A number that is either equidigital or frugal

Frugal number

A frugal number is a natural number that has more digits than the number of digits in its prime factorization . For example, using base-10 arithmetic, the first few frugal numbers are 125 , 128 , 243 , and 256...

is said to be economical.