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
On Sunday, March 21, 2021 at 11:34:51 AM UTC-5 [email protected] wrote:
> 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.
>
> On Fri, Mar 19, 2021 at 11:27 PM Chris Smith <[email protected]> wrote:
>
>> It will help me see what your conditions are if you can show how the
>> method works for 61, 109, 149 and 163.
>>
>> /c
>>
>> On Friday, March 19, 2021 at 12:45:53 PM UTC-5 [email protected] wrote:
>>
>>> 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
>>>
>>> On Fri, Mar 19, 2021 at 11:08 PM Janmay Bhatt <[email protected]>
>>> wrote:
>>>
>>>> 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
>>>>
>>>> On Fri, Mar 19, 2021 at 10:05 PM Chris Smith <[email protected]> wrote:
>>>>
>>>>> 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
>>>>> <https://en.wikipedia.org/wiki/Law_of_small_numbers#:~:text=%20Law%20of%20small%20numbers%20may%20refer%20to%3A,small%20numbers%0AThe%20tendency%20for%20an%20initial...%20More%20>"
>>>>>
>>>>> give false assurance, but I would love to be wrong.
>>>>>
>>>>> /c
>>>>>
>>>>> On Friday, March 19, 2021 at 8:55:48 AM UTC-5 [email protected]
>>>>> wrote:
>>>>>
>>>>>> 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
>>>>>> On Friday, 19 March 2021 at 05:14:37 UTC+1 [email protected] wrote:
>>>>>>
>>>>>>> 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)
>>>>>>>
>>>>>>> On Thu, Mar 18, 2021 at 9:45 PM Chris Smith <[email protected]>
>>>>>>> wrote:
>>>>>>>
>>>>>>>> What would be the result of starting with primes 29, 41 or 43?
>>>>>>>>
>>>>>>>> /c
>>>>>>>>
>>>>>>>> On Wednesday, March 17, 2021 at 7:33:38 PM UTC-5 [email protected]
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>> 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 <[email protected]>
>>>>>>>>> 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
>>>>>>>>>
>>>>>>>>> > Kindly guide me for this.
>>>>>>>>> >
>>>>>>>>> > On Thu, Mar 18, 2021 at 1:30 AM Aaron Meurer <[email protected]>
>>>>>>>>> wrote:
>>>>>>>>> >>
>>>>>>>>> >> 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
>>>>>>>>> >>
>>>>>>>>> >> On Mon, Mar 15, 2021 at 12:44 PM Janmay Bhatt <
>>>>>>>>> [email protected]> wrote:
>>>>>>>>> >> >
>>>>>>>>> >> > 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.
>>>>>>>>> >> >
>>>>>>>>> >> > --
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>>>>>>>>> https://groups.google.com/d/msgid/sympy/4183d41e-49cf-41c3-8ea1-d04514f2143cn%40googlegroups.com.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> >>
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>>>>>>>>>
>>>>>>>>>
>>>>>>>>> >
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>>>>>>>>> https://groups.google.com/d/msgid/sympy/CA%2Bceb0zMWkCdaDJr9EZFi0BSFXky-sSJ-M23Wvdbga6YRDHrCQ%40mail.gmail.com.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
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>>>>>>>> To unsubscribe from this group and stop receiving emails from it,
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>>>>>>>>
>>>>>>> To view this discussion on the web visit
>>>>>>>> https://groups.google.com/d/msgid/sympy/7c533357-122e-4c7b-82ab-0f983657f4e6n%40googlegroups.com
>>>>>>>>
>>>>>>>> <https://groups.google.com/d/msgid/sympy/7c533357-122e-4c7b-82ab-0f983657f4e6n%40googlegroups.com?utm_medium=email&utm_source=footer>
>>>>>>>> .
>>>>>>>>
>>>>>>> --
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>>>>> .
>>>>>
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> To view this discussion on the web visit
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