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Message boards : Problems and Help : Проблема Серпинского

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ammo77

Joined: 20 Aug 22
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Message 156759 - Posted: 20 Aug 2022 | 22:09:13 UTC

Теперь чтоб ускорит процесс проверки настроим и уберем не нужные
числа берем кандидат
1+21181*2^(n)
и получаем числа для проверки только в этих последовательностях
могут быт простые числа .

1+21181*2^(68+120n)
1+21181*2^(80+120n)
1+21181*2^(92+120n)
1+21181*2^(44+120n)

Но с уверенностью можно сказать что простое число есть в них в каждой по отдельности .
Я бы выбрал для проверки одну из них.
Если интересно и так не искали могу настроит любой кандидат меньший и больше .

____________

Ravi Fernando
Volunteer tester
Project scientist

Joined: 21 Mar 19
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Message 156762 - Posted: 21 Aug 2022 | 1:43:35 UTC - in response to Message 156759.

Copying from Google Translate for those of us who don't speak Russian:

Now, in order to speed up the verification process, we will configure and remove unnecessary
numbers take the candidate
1+21181*2^(n)
and get numbers to check only in these sequences
may be prime numbers.

1+21181*2^(68+120n)
1+21181*2^(80+120n)
1+21181*2^(92+120n)
1+21181*2^(44+120n)

I think "80" is a typo: 1+21181*2^(80+120n) is always divisible by 17. On the other hand, 1+21181*2^(20+120n) does not generally have any small factors. But other than that, yes, these are the only exponents that can produce Proth primes with k=21181, because all other candidates are divisible by a prime p <= 17.

This is an example of sieving: removing candidates that are divisible by small prime numbers. For the Seventeen or Bust project, the sieving was done in the (now suspended) PSP Sieve subproject, which appears to have gone up to p ~ 104P = 104 * 10^15. So all candidates that are divisible by a prime of this size or smaller have already been removed from the search, and we are only testing the remaining (possibly prime) candidates in SoB.
But we can say with confidence that a prime number is in them in each separately.

Very likely true--but surely Seventeen or Bust is hard enough already!
I would choose to test one of them.
If you are interested and have not looked for it, I can set up any candidate, smaller and larger.

I would encourage you to run the Seventeen or Bust subproject if you're interested in this. A lot of smart people (and a lot of fast computers) have worked hard to make the search run as efficiently as possible. There's no need to reinvent the wheel.

ammo77

Joined: 20 Aug 22
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Message 156765 - Posted: 21 Aug 2022 | 2:42:54 UTC - in response to Message 156762.

Copying from Google Translate for those of us who don't speak Russian:
[quote]Now, in order to speed up the verification process, we will configure and remove unnecessary
numbers take the candidate
1+21181*2^(n)
and get numbers to check only in these sequences
may be prime numbers.

1+21181*2^(68+120n)
1+21181*2^(80+120n)
1+21181*2^(92+120n)
1+21181*2^(44+120n)

I think "80" is a typo: 1+21181*2^(80+120n) is always divisible by 17. On the other hand, 1+21181*2^(20+120n) does not generally have any small factors. But other than that, yes, these are the only exponents that can produce Proth primes with k=21181, because all other candidates are divisible by a prime p <= 17.

Да там 1+21181*2^(20+120n) где могут быт простые числа спасибо что
исправили .

Я предлагаю систему закономерности простых чисел близнецов и Софи
Жермен как единую систему на платформе идеального модуля для этой задачи.

Так же классификацию простых чисел ,по видам чисел с минимальным кольцом
факторизации для каждого вида отдельно и их концам 1-3-7-9 .
Платформа так же доказывает бесконечность простых чисел близнецов и С.Жермен
новым методом и формулами .
Куда мне обращаться чтоб показать эти методы? прощу посодействовать и перенаправит
меня к специалистам теории чисел чтоб они проверили новый метод .

Scott Cox

Joined: 3 Aug 16
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Message 156988 - Posted: 15 Sep 2022 | 8:46:13 UTC - in response to Message 156765.

Yes, there 1+21181*2^(20+120n) where prime numbers can be, thanks for that
fixed .

I propose a system of laws of prime numbers of twins and Sophie
Germain as a single system on the platform of an ideal module for this task.

Also the classification of prime numbers, according to the types of numbers with a minimal ring
factorization for each species separately and their ends 1-3-7-9 .
The platform also proves the infinity of twin primes and S. Germain
new method and formulas.
me to specialists in number theory so that they check the new method.

All you need to do is simply run the programs on this website to find prime numbers of this type, if that is what you are asking. It sounds like you may be interested in the twin prime conjecture. If you are saying that you have found some interesting new ideas about prime sieving, Wikipedia and scholarly publications can help. For example:

https://en.wikipedia.org/wiki/List_of_prime_numbers#Sophie_Germain_primes
https://ru.wikipedia.org/wiki/Список_простых_чисел
https://annals.math.princeton.edu/

я надеюсь что это поможет вам. (I hope that this helps you.)

Message boards : Problems and Help : Проблема Серпинского