Discovering the Prime and Factored Parts of Positive Integers

In summary, if one can calculate the factor of a system greater than one, then it is possible to calculate the prime parts of the system.
  • #1
lostcauses10x
87
0
Is there a way within reasonable errors to say what part of the positive integers are prime and what part is factored greater than one? Oh course one is a factor of all numbers greater than zero.

Yeats ago playing around a floating constant became known to me. to the tenth decimal place is was .7052311717917 and so on depending on what point in the system a prime was a total position of in; it is a ratio of the number system if factoring greater than 1 is calculated..
Tthis of course was what i calculated as the factor part of the positive real integers,
ring a bell to any one?

Two part question, sorry.

Andas usual I most likely lost most people. If so my apologies. .

For once I will try and explain.
Simply put some one years ago asked what part of the whole positive integer system was prime. I of course could not answer such. Yet it made me think.
I came up with : if I can not come up with the total prime part could it be possible to come up with the factor part of the system greater than one, of course leaving the primes within a reasonable error factor. Oh course I am sure I am not the first to come up with the idea, So were can I find this?
The number I gave above is what I calculated the system to be of the factored part, other than one of course.
 
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  • #2
lostcauses10x said:
Is there a way within reasonable errors to say what part of the positive integers are prime and what part is factored greater than one? Oh course one is a factor of all numbers greater than zero.

Yeats ago playing around a floating constant became known to me. to the tenth decimal place is was .7052311717917 and so on depending on what point in the system a prime was a total position of in; it is a ratio of the number system if factoring greater than 1 is calculated..
Tthis of course was what i calculated as the factor part of the positive real integers,
ring a bell to any one?

Two part question, sorry.

Andas usual I most likely lost most people. If so my apologies. .

For once I will try and explain.
Simply put some one years ago asked what part of the whole positive integer system was prime. I of course could not answer such. Yet it made me think.
I came up with : if I can not come up with the total prime part could it be possible to come up with the factor part of the system greater than one, of course leaving the primes within a reasonable error factor. Oh course I am sure I am not the first to come up with the idea, So were can I find this?
The number I gave above is what I calculated the system to be of the factored part, other than one of course.
See http://en.wikipedia.org/wiki/Prime-counting_function
 
  • #3
ramsey2879
Thanks for the reply.

Of course a system that could tell were the next prime is, would be great for what I did. Instead of a table of known primes such could be used to calculate what I did here to some un believable lengths.

if one is a periodic position on the entire number line that for the positive integers it is an intersection will all the prime integers,
then 2 is also a periodic intersection of the whole set of positive integers such that its intersection is 1/2 the system plus or minus 1 divided by infinity. ( the last part due to we do not know if the system would end in odd or even.)
So what part of the system does 3 intersect?
 
  • #4
Weell strange I don't find anything on this

2 is 1/2 of the system covered.
3 unto itself would be 1/3 of the system covered or 1/3
yet every other 3 is already covered by 2, so 1/3 dived by 2 = 1/6
So 1/2 plus 1/6 equals 4/6.

Asimple pater happens
2 is 1/2 , 3 is 4/6, 5 is 21/ 30, 7 is 148/210, and so on..

Note it is easier to leave the fraction ( ratio as whole instead of reducing them
This is simply due to both the numerator and denominator can be multiplied by the next prime. of course.
The numerator is then just plus 1.

It is such the changes in the gain of each prime is added to the situation yet using just a 1 over the denominator ( the actual coverage of the previous prime intersecting already. to the new intersected portions of the system to see how they change rapidly.)

2 is 1/2 then 3 is 1/6, 5 is 1/30, 7 is 1/210, 11 is 1/ 2310,13 is1 30030, and so on. It gets to be a very small increase very rapidly.

If some one sees were I am wrong or gust plain crazy let me know.

It is easy to see that the larger a prime number used for factor, it rapidly unto itself becomes smaller, ( 1/2, 1/3. 1/5, 1/7, 1/11 1/13. With the part that is intersected by previews numbers and no gain by such intersection, to removing part of the system: then the method I have used should be valid.

The question then becomes does it converge??
m
 
  • #5


I find this question intriguing and worthy of further exploration. While it may be difficult to accurately determine the exact percentage of positive integers that are prime and those that are factored greater than one, it is certainly possible to estimate this with reasonable errors.

One approach to this problem could be to use statistical analysis and probability theory. By studying the distribution of prime numbers and factored numbers within the positive integer system, we could make predictions about the likelihood of a given number being prime or factored. This would allow us to estimate the percentage of primes and factored numbers within the system.

Another approach could be to use computational methods to analyze large sets of positive integers and determine their prime and factored properties. This could provide a more accurate representation of the overall distribution of primes and factored numbers within the system.

It is also worth noting that the concept of "reasonable errors" is subjective and can vary depending on the context and purpose of the analysis. For example, if we are looking at the percentage of primes and factored numbers in a small range of numbers, our margin of error may be smaller compared to if we were looking at the entire range of positive integers.

In terms of previous research on this topic, there have been numerous studies and theories proposed on the distribution of primes and factored numbers within the positive integer system. Some famous examples include the Prime Number Theorem and the Goldbach Conjecture. However, there is still much to be explored and discovered in this area.

In conclusion, while it may be challenging to determine the exact percentage of primes and factored numbers within the positive integer system, with the use of various analytical and computational methods, we can estimate this with reasonable errors and continue to deepen our understanding of the properties of positive integers.
 

Related to Discovering the Prime and Factored Parts of Positive Integers

1. What is a prime number?

A prime number is a positive integer that is only divisible by 1 and itself. In other words, it has no other factors except 1 and itself.

2. How do you determine if a number is prime?

To determine if a number is prime, you can divide it by all numbers between 2 and the number itself. If the number is only divisible by 1 and itself, then it is prime. Otherwise, it is a composite number.

3. What is the difference between prime and composite numbers?

A prime number has only two factors, 1 and itself, while a composite number has more than two factors. In other words, a composite number can be divided evenly by numbers other than 1 and itself.

4. How do you find the prime factorization of a number?

To find the prime factorization of a number, you can use a factor tree or divide the number by prime numbers until you are left with only prime factors. The prime factors are then multiplied together to get the prime factorization.

5. Why is it important to know the prime factorization of a number?

Knowing the prime factorization of a number can help in several ways, such as simplifying fractions, finding the greatest common factor, and determining if a number is prime or composite. It is also essential in cryptography and number theory.

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