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# Eps 59: Prime number

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The standard evidence attributed to Euclid states that, since there is a finite set of prime numbers, a number must be divisible by a prime and must have prime factors, which leads to a direct contradiction. Note that we cannot define a "prime" or simply "prime" to be a positive integer with positive dividers only, because there are no positive integers, only negative ones. There is no prime composite, since the only factors of a natural number are those of natural numbers and not any other number in the set.
A prime number, often simply called "prime," is a positive integer that has no other positive dividers than 1. It is not a divisible integer greater or less than, and it is divisible only by one of the prime numbers. In other words, a number is prime if and only if it is only the number that cannot be considered by another number.
For example, only the dividers of 13 are divisible by 1 and 13, which makes 13 a prime, while the number 24 has no corresponding factorization, which makes 24 not a prime.
While the term "prime" generally refers to a positive integer number, other prime numbers can also be defined. To find out if a number is prime, try dividing it yourself, and if it is exactly divisible by another number, then it is prime. Otherwise the numbers are either prime numbers or no prime numbers, but either way they must be abes prime numbers to be divisible by any number.
According to this definition, a prime is a number greater than 1, which is divided by only another prime number over 1. It is an integer that has the same number of digits as the number 1, but a different number of the order of 1 - 2.
In other words, a prime can be divided equally by another prime and vice versa. For example, 3 is a prime number because it cannot be divided equally by the numbers 1 - 3. On the other hand, 6 is also a prime number, because 6 can divide 2 and 3 equally, but not by 1 and 2, nor by 3 and 1.
A prime is odd if even numbers are divisible by 2, which makes it composed. The difference between two prime numbers in a row is therefore at least 2. From this list it is clear that all successive prime numbers are exactly 2 without any change.
Suppose we found all prime numbers and we generate a list of all numbers from 2 to n. Starting with the smallest prime p , we delete all multiples of 2 from the 2 list.
A prime is a number greater than 1 that has exactly two factors and a composite number is if and only if it has more than two factors. Similarly, we assign the prime of all numbers with size 2 to the next value of p and assign it the same number as p.
For this reason, many people state that a prime must be greater than 1, and that the only count that is counted is the prime of all numbers above 1.
The above definition implies that any number or natural number that has more than two factors and is greater than 1 is a composite number, but not a prime. For example, if p is the prime of all natural numbers above 1 and p = 0.5, then we can say that p is p-1. If p = -1, one could also say that the count of a number above p, even if it is not a prime number because it is composed, is such a number. This means that if and only if there is a p of p for each p and no longer p + 1, the natural number 1 cannot be prime!
Since 2 is the divider of all even numbers, any even number greater than 2 has the same number of factors as p and no more factors than p .
No integer greater than 1 can be included in a unique set of prime numbers, and no other even number is a compound, except positive multiples of 3 and 3, which are composed. If one of these numbers is divisible only by the number 1, then it is prime, but all other even numbers are not because they are composed.
We will use the Eratosthenes sieve to detect the prime numbers from 1 to 100, and then a sieve for the remaining numbers.
If we use a grid, it is clear that 1 is not a prime number, because its only factor is 1, and all other prime numbers must be odd. If 2 is divisible by 2, 1 cannot be a prime, but any other even number can be a prime as long as it is divisible by 2. If 1's only factors are 1 and 1 + 2 + 1 = 2, it can also be the prime number.