Is there a ¨periodic table¨ for numbers?

Question

Is there a best way to organize numbers so that it identifies the most traits within each number?

(edit for clarification): a multiplication table gives simple detail to help understand multiples and divisors. Is there a more dynamic table that gives more detail to each number?

For instance, a multiplication table with only primes on the axis or maybe a slide rule could be argued to be an organization of numbers that gives a lot of insight.

Answer 1

There have been a few sites that attempt to organize numbers by their qualities. See what you think of each of the following approaches:

What's Special About This Number?

Number Gossip

The Secret Lives of Numbers

Notable Properties of Specific Numbers

Zoo of Numbers

The Database of Number Correlations: Properties and Meanings

Wikipedia's Integers Category

Prime Curios

The On-Line Encyclopedia of Integer Sequences

Answer 2

The short answer to your questions is: no, there isn't a periodic table of numbers.

However, there a certainly many numbers that share similar properties. But it is hard to organize this when one hasn't established what properties your are interested in.

However since all natural numbers have a unique decomposition into a product of prime numbers, prime numbers could be thought of as building blocks of the whole numbers. As such many "properties" of numbers can be answered in terms of prime numbers. In fact the study of prime numbers has for a long time fascinated mathematicians (and non-mathematicians). There are still many unanswered questions relating to prime numbers. My point is that one approach to a "periodic table" of numbers could focus on prime numbers.