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Numbers can measure the length of segments, which fit into one another.
This spreadsheet in the picture represents the length of the numbers, and counts each unit of a number as a cell in the spreadsheet. Every time 1 appears in the cell, that cell is a factor of the number on the left.
You can see how many factors a number has, and which factors a number has (every time 1 appears, the factor is on the top of the column).
If a number (the raw of the number) has only two cells with value 1, that number is a prime. The cells with value 1 appear in column C (representing number 1), and in the column of the number itself.
The first column is always a factor and has always value 1, as 1 is always a factor of any natural number.
The length of a factor is the same of the distance between two cells with value 1.
A segment fits into another one if it has the same size, or half of the size (for even numbers) or less than half (for composite numbers). Therefore cells with value 1 never appear in the second half of the numbers.


 
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Primes numbers are divisible only by 1 and by themselves. Is it possible to to predict where primes will appear in the series of natural numbers 1,2,3...?
Some people believe that there are hidden patterns in the series of prime numbers, which still need to be discovered, and which will allow us to calculate where prime numbers appear in the series.
If the only divisors of natural numbers were 0,1,2 and 3, and if we considered 5 and numbers bigger than 5 not as a divisors, but only as natural numbers to be divided, we would have a regular pattern in primes. All prime numbers are odd (with the exception of 2), because every even number is divisible by 2 (therefore has at least 3 factors (1,2 and itself). If you divided the series of odd numbers by 3,  one third of the odd numbers would be divisible by 3. We could find the primes by a process of exclusion: we would know that only the odd numbers include the primes, and that every odd number which is not a multiple of 3 would be a prime (apart from 2), so it would be easy to calculate primes. For example, the first primes would be 2,3,5,7,11,13,17,19,23,25,29, 31,35,37,41,43,47,49,53,55 etc.
To find the primes, we would start from 5, and add first 2, then 4 (alternately), and we would find the next prime number.
However, when we use number 5 as a prime and as a new divisor (together with 3), we  generate irregularity and randomness in the previous series, as multiples of 5 will make composite (and not primes any more) new numbers from the previous series, like 25, 35, 55 etc. As a consequence, we would have to remove these numbers from the initial series. It would be like finding random holes in a road where holes appeared regularly every 2 odd numbers.

When we introduce 7 as a prime divisor, we will find more odd composite numbers that are not divisible by 3 or 5, but are divisible by 7, like 49, 77,91 etc. We would have to remove these numbers as well, and more random holes would appear on the road.

As we use more and more primes as divisors (11,13, 17, 19 etc.), we will find new odd numbers in our initial series that are divisible only by these new primes, for example, the odd number 209 (which is divisible only by 11, and not any previous prime); the odd number 247 (which is divisible only by 13 etc). Therefore we will have to remove these numbers from our initial list of primes, and more and more numbers will have to be removed, as as we keep finding random new primes.

Euclid demonstrated that there are  infinite primes.  Therefore there are infinite new unique divisors of infinite new odd numbers, which causes infinite randomness in the series.

I suspect that a finite number of primes is not enough to generate all the unique prime factors. For any given prime number p1, you can find a composite odd number n which equals p1*p1, and is divisible only by p, and is not divisible by any other prime smaller than p (and it's the square of a prime, having as factors 1, itself, and the prime p).

In other words, you don't know how many odd numbers you will have to remove from our initial series, therefore you can't predict where new holes will appear in the initial series. In fact, they proved that there are a number of consecutive holes (consecutive composite numbers) in the series of natural numbers as big as any given natural number, by using an proof similar to the one used by Euclid to show that there are infinite primes.

Since there are infinite primes, there are infinite numbers divisible by primes, and we can always find a new prime p which is the only divisor of the odd number n (when p1*p1 =n).



 
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The artichoke uses the Fibonacci pattern to spiral the sprouts of its flowers. The Fibonacci series starts with 0 and 1, and each of the following integers is the sum of the previous two numbers. Therefore, the numbers of the Fibonacci series are the following:
0,1,1,2,3,5,8,13,21,34,55 etc.
In the Fibonacci series you can also find the next number of the series by multiplying the previous number by an irrational number, which, as the numbers get bigger and bigger, becomes approximately 1.6180339887 (or 1.6180339887...), and which is called the Golden ratio.  Furthermore, you can find the previous number of the series by multiplying the next number by approximately 0.6180339887, which is the inverse of the golden ratio (1/1.6180339887 ).
What's the link between the Artichoke and Fibonacci? The artichoke sprouts its leafs at a constant amount of rotation, which is always 222.5 degrees (in other words the distance between one leaf and the next is 222.5 degrees), and you can measure this rotation by dividing 360 degrees (a full spin) by the inverse of the golden ratio. That's why the artichoke uses the Fibonacci series.