Series of Primes

[Janmay Bhatt]

Hello there,

I want to add the function for prime number generation which

provides the series of primes and prime number.

You might think how do we get series of prime numbers?

That's what my topic was...

I have my published research in IJMTT of prime conjecture which 

you can see here.

This proves that primes are not random but has series which greatly 

helps for science and scientists.

Please guide for same.

[Chris Smith]

Perhaps, as proof of concept, write a function `my-primerange(a,b)` which computes primes in [a,b) and compare the results to the current implementation of `primerange(a,b)`.

/c

[Aaron Meurer]

I'm having a difficult time understanding the paper you linked to. Can
you give an example input and output for the function you are
suggesting?

Aaron Meurer

> --
> You received this message because you are subscribed to the Google Groups "sympy" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to sympy+un...@googlegroups.com.
> To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/4183d41e-49cf-41c3-8ea1-d04514f2143cn%40googlegroups.com.

[Janmay Bhatt]

Surely I can give an example of a function by taking a prime number as 19 for base.

I am attaching my paper herewith for reference, in which you may refer function

Prime gaps for 19 are 2 and 4 (i.e our a and b in pole point section)

According to the function we have 2(19) - 17 = 21 (not prime)

now second part,

2(19) -13 = 25 (not prime)

now third part,

2(19)-1 = 37 (prime)

So we generated a prime from a prime which can be started from 2

and recursively we will get a series of primes for a specific base.

Then with the same notations we have addition formulation for series and nth term formulation.

Now to make this function in python for sympy I am still trying to make the function complete

for which I thought of GSOC.

Kindly guide me for this.

You received this message because you are subscribed to a topic in the Google Groups "sympy" group.
To unsubscribe from this topic, visit https://groups.google.com/d/topic/sympy/Od8RB0hn9ws/unsubscribe.
To unsubscribe from this group and all its topics, send an email to sympy+un...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6L_-bZwvKvLS86wnK9fSqe8OzqH6qZpQNWOYSFxBT6uPA%40mail.gmail.com.

[Aaron Meurer]

I still don't understand and I am not able to follow the paper either.
Can you give an example of what the function call would look like for
your example? Like yourfunction(x) == y.

On Wed, Mar 17, 2021 at 4:47 PM Janmay Bhatt <jrbhat...@gmail.com> wrote:
>
> Surely I can give an example of a function by taking a prime number as 19 for base.
> I am attaching my paper herewith for reference, in which you may refer function
> Prime gaps for 19 are 2 and 4 (i.e our a and b in pole point section)
> According to the function we have 2(19) - 17 = 21 (not prime)
> now second part,
> 2(19) -13 = 25 (not prime)
> now third part,
> 2(19)-1 = 37 (prime)

It's known that there exists a prime between any x and 2x, but where
do 17, 13, an 1 come from? And how does 4 relate to anything?

>
> So we generated a prime from a prime which can be started from 2
> and recursively we will get a series of primes for a specific base.
>
> Then with the same notations we have addition formulation for series and nth term formulation.
>
> Now to make this function in python for sympy I am still trying to make the function complete
> for which I thought of GSOC.

GSoC projects are typically larger in scope than a single function,
unless the algorithm required for the single function is very complex.
But I still don't understand what this function of yours even is or
what use it would have. Is it an existing function or algorithm in the
literature (outside of your paper)? Is the purpose just to generate
prime numbers? SymPy has the function randprime(), although I'm sure
the methods used by it could be more efficient for large primes.

Aaron Meurer

> To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CA%2Bceb0zMWkCdaDJr9EZFi0BSFXky-sSJ-M23Wvdbga6YRDHrCQ%40mail.gmail.com.

[Chris Smith]

What would be the result of starting with primes 29, 41 or 43?

/c

[Janmay Bhatt]

for 29 first section will give 58-23=35(not prime)

second section gives 58-19=39(not prime)

third section gives 58-polepoint

where polepoints are 3 and 5 as prime gaps for 29 are 2 and 6

Therefore 58-3=55(not prime) but 58-5=53 is prime.

similarly for 41 first two cases will not give primes but in polepoint 

polepoint will be 1 and 3 as gaps are 2 and 4

so for 3rd section 2*41 - 1 = 81(not prime)

but 2*41 - 3 = 79 (prime)

same for 43,

pole points will be 1 and 3 as gaps are 2 and 4

so for 3rd section

2*43 - 1 = 85(not prime)

but 2*43 - 3 = 83(prime)

To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/7c533357-122e-4c7b-82ab-0f983657f4e6n%40googlegroups.com.

[nijso.be...@gmail.com]

How is this method useful if it doesn't uniquely generate a prime? How do you know if a generated number is prime or not? Is the goal of the method to give you prime numbers or just a bunch of numbers that may or may not be prime? How is this better than just having the series 1,2,3,4,5,... :

1(not prime), 2(prime), 3(prime), 4(not prime), 5(prime), ...

Best regards,

Nijso

[Chris Smith]

  Could you show how the method works for 61, 109, 149 and 163, please?

[Chris Smith]

The method is useful if, knowing 4 primes you can, with a small number of test, guarantee another prime. I suspect that this is not the case and that we are seeing the "law of small numbers" give false assurance, but I would love to be wrong.

/c

On Friday, March 19, 2021 at 8:55:48 AM UTC-5 nijso.be...@gmail.com wrote:

[Janmay Bhatt]

This is mainly useful for encryption

To generate larger unpredictable but same type number

Also to send false data from machine when someone tries to hack the system

To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/37801059-8d8d-4a1f-bc39-daaeae473755n%40googlegroups.com.

[Janmay Bhatt]

I can understand that this idea has many condition(but always correct and accurate)

But the main idea is to run this for first time and save the data so that the run time is less

That's why I want to propose this idea in GSOC for better upgradation and make a step ahead

[Chris Smith]

It will help me see what your conditions are if you can show how the method works for 61, 109, 149 and 163.

/c

[Janmay Bhatt]

This all examples are of pole point which are to be done exactly same way I did in trailing mails.

By looking to the examples I can observe that pole point is not clear.

So I request to read pole point theory in my paper which I have send in trailing mail.

To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/a53def32-03a0-4bf5-98ea-544a4e2e907dn%40googlegroups.com.

[Chris Smith]

It would be better for you to demonstrate as the paper doesn't provide any clarity regarding the use of pole point(s). Here is what I understand the paper to be saying:

It says pole points are "x" and "1" were x is in {a + 1, b - 1}. So take n' = 61 which is preceded by primes 53 and 59. "a" and "b" are 59-53=6 and 61-59=2 so pole points are 7 and 1 but neither `2*61 - 7` nor `2*61 - 1` (nor `2*61-5` nor `2*61 - 3`, allowing for sign error in pole-point definition) are prime.

So it still appears that your hope that this method will generate primes efficiently is based on success with small numbers. You have not demonstrated with large numbers that this will work reliably. It is just as likely that subtracting *any* odd number from twice a known prime will lead, occasionally, to a prime. I have not yet seen any assurance that the method hinted at in the paper is better than guessing.

/c