# Feminine numbers and the importance of set reproduction in prime numbers and factorization.

Numbers ending in 1, 3, 7, or 9 have a special tendency. Their behavior is also of great consequence to prime numbers and the difficulties with integer factorization.

Consider how important the last digit of a number is. The final digit defines a critical property about the number, such as whether it’s even or odd. No other digit provides this sort of insight or influences the nature of how to work with it so profoundly.

So let’s consider why numbers ending in 1, 3, 7, or 9 deserve their own special subset. For now, let’s call them feminine numbers.

When you multiply two feminine numbers together, the result is always another feminine number. That is, the result will end in 1, 3, 7, or 9. Go ahead, try it. 13 times 27? 351. It’s works every time.

`Multiplication Chart of Feminine Numbers╔═══╦═══╦═══╦═══╦═══╗║   ║ 1 ║ 3 ║ 7 ║ 9 ║╠═══╬═══╬═══╬═══╬═══╣║ 1 ║ 1 ║ 3 ║ 7 ║ 9 ║║ 3 ║ 3 ║ 9 ║ 1 ║ 7 ║║ 7 ║ 7 ║ 1 ║ 9 ║ 3 ║║ 9 ║ 9 ║ 7 ║ 3 ║ 1 ║╚═══╩═══╩═══╩═══╩═══╝`

I call this tendency set reproduction. The same tendency also exists for numbers ending in 5, numbers ending in 0, or the masculine numbers (numbers ending in 2, 4, 6, or 8). When multiplying two numbers within their same set, it will always produce another value within that same set — and all combinations of that set get cycled.

`Multiplication Table for Masculine Numbers╔═══╦═══╦═══╦═══╦═══╗║   ║ 2 ║ 4 ║ 6 ║ 8 ║╠═══╬═══╬═══╬═══╬═══╣║ 2 ║ 4 ║ 8 ║ 2 ║ 6 ║║ 4 ║ 8 ║ 6 ║ 4 ║ 2 ║║ 6 ║ 2 ║ 4 ║ 6 ║ 8 ║║ 8 ║ 6 ║ 2 ║ 8 ║ 4 ║╚═══╩═══╩═══╩═══╩═══╝`

So what does this matter? Well, if nothing else it’s interesting. But prime numbers are a big deal in mathematics. Understanding why they exist and seeing the patterns that emerge from numbers can help us appreciate why. And feminine numbers are one of the most critical keys to understanding primes.

While the terms “masculine” and “feminine” may not be a perfect nomenclature for the sets they represent, they should nevertheless be distinguished from even and odd sets.

From a genetic standpoint, feminine numbers could also be considered recessive, while all of the non-feminine numbers could be considered dominant. However, there are also important points to consider about how these sets exert dominance — which I will describe in a later post.