syndicatel
New member
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- Dec 11, 2023
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This is a repost from one forum member from another mathematical forum. I'll try to translate it into English (as best I can). [this is a text from another person on the forum]:
Since Petrov is being quoted here, he also has a much more interesting article devoted to prime numbers: “Petrov I.B. METAREMULTION (general superficial numerical study of an interesting prime number)” Author’s article, self-publishing, 2023, 5 pp. (attached to topic). [I read it, but, alas, it is only in Russian (you can translate it through a translator)].
Actually, the author there cites the so-called metaremultion or multi re-near-repdigits:
Yes, Petrov gives the following hypothesis:
I am writing from myself:
The topic seemed quite interesting to me. But the problem is that it is not so easy to factor large metaremultions. I'm trying to write a program to test a number for primality by adding "7" to the last one from the article and checking. So far I have added/checked about ~ 5000 “7” added to the last number - there are no simple ones. But the accuracy of the program algorithm is very low.
Since Petrov is being quoted here, he also has a much more interesting article devoted to prime numbers: “Petrov I.B. METAREMULTION (general superficial numerical study of an interesting prime number)” Author’s article, self-publishing, 2023, 5 pp. (attached to topic). [I read it, but, alas, it is only in Russian (you can translate it through a translator)].
Actually, the author there cites the so-called metaremultion or multi re-near-repdigits:
This is a number with a cyclic digital recording of blocks 277...7, that is, the number is formed by adding block 277...7 to the original (2777), and the number that appears when adding such a block is also simple. For the given number it is:
[this is a text from another person on the forum]: Each one is simple. This is actually very interesting!! The author of the article provides a small study and for these numbers displays a sequence in increasing order of digit capacity (you can see the formula in the article). Yes, of course, for the next number this sequence is not correct, since its subsequent term is equal to ~196, which is less than the digit capacity of the last number found by the author. But, if there are no such metaremultion numbers at all, then their entire sequence fits into a certain formula! This suggests that at least some of the prime numbers have an absolutely definite (not random) distribution.Unfortunately, I do not have sufficient programming skills to test such “metaremultions” beyond the number that the author stopped at. And checking them using standard mathematical utilities is already quite difficult due to the large digit of numbers. We need an algorithm to quickly check for simplicity. But for some reason it seems to me that this is a finite sequence of prime numbers and the author has actually already found them all. It would be great because there is a sequence of bits.
Yes, Petrov gives the following hypothesis:
But I don't think it's true. In fact, all series of prime numbers driven into the framework of complex structures (such as metaremultion) are finite. But I could be wrong, in general the topic is interesting.
I am writing from myself:
The topic seemed quite interesting to me. But the problem is that it is not so easy to factor large metaremultions. I'm trying to write a program to test a number for primality by adding "7" to the last one from the article and checking. So far I have added/checked about ~ 5000 “7” added to the last number - there are no simple ones. But the accuracy of the program algorithm is very low.