Search prime numbers by dimension

[claugoru]

Good morning

My name is Claudio Govi ​​and I am an Italian who lives in Portugal. I joined this forum to publish a new method of research on prime numbers. The method I would like to publish differs from the other methods because it looks for prime numbers in a dimension and no longer as a single number. This method will give me two advantages. The first is that the numbers found will all be 100% prime . The second advantage is that I can do without probabilistic or primality tests.

Before publishing it, however, I ask the courtesy to confirm the following ...
When I search for a very large prime number, the first thing I do is to try, through probabilistic tests, to identify a prime candidate that gives me a high probability of being prime. Then I run the test with a sieve and confirm or deny that the number is prime or not. Right?

In the search by dimension this does not happen. In this search, all the prime numbers within it are securely identified.

My computer is a small computer with very limited computing power. It takes almost an hour and a half to prove that a number of only 23 digits is a safe prime.

In the search by dimension, however, this happens ...

N = 23-digit number (10100010001000100001089) X = 100,000 (dimension)
Total calculation hours 5:30. Safe primes found 2026
Calculation hours for each prime number found 0: 0: 10


Thanks for your attention

[paulunderwood]

Originally Posted by claugoru

Good morning

My name is Claudio Govi ​​and I am an Italian who lives in Portugal. I joined this forum to publish a new method of research on prime numbers. The method I would like to publish differs from the other methods because it looks for prime numbers in a dimension and no longer as a single number. This method will give me two advantages. The first is that the numbers found will all be 100% prime . The second advantage is that I can do without probabilistic or primality tests.

You will have to elaborate what it means to "look for a primes in a dimension".

Before publishing it, however, I ask the courtesy to confirm the following ...
When I search for a very large prime number, the first thing I do is to try, through probabilistic tests, to identify a prime candidate that gives me a high probability of being prime. Then I run the test with a sieve and confirm or deny that the number is prime or not. Right?

Usually sieving. trail factoring, other factoring methods, PRP test and proof test is the order.

In the search by dimension this does not happen. In this search, all the prime numbers within it are securely identified.

My computer is a small computer with very limited computing power. It takes almost an hour and a half to prove that a number of only 23 digits is a safe prime.

You will have to be definitive about what you mean by a "safe prime".

In the search by dimension, however, this happens ...

N = 23-digit number (10100010001000100001089) X = 100,000 (dimension)

This is bordering on non-mathematical gibberish. Please be more explicit.

Total calculation hours 5:30. Safe primes found 2026
Calculation hours for each prime number found 0: 0: 10

Pari/GP can prove such small primes in less than a millisecond even on slow hardware.

Thanks for your attention

I am sure we look forward to your findings.

[Dr Sardonicus]

Originally Posted by claugoru

<snip>
In the search by dimension, however, this happens ...

N = 23-digit number (10100010001000100001089) X = 100,000 (dimension)
Total calculation hours 5:30. Safe primes found 2026
Calculation hours for each prime number found 0: 0: 10
<snip>

It appears that you're looking for primes in a short interval. The following Pari-GP scripts are incredibly inefficient. They only exclude multiples of 2, 3, or 5. The isprime() script is noticeably slower because prime-proving is much slower than BPSW compositeness testing. But neither took long enough for me to be drumming my fingers

? n=10100010001000100001089;c=1;forstep(i=2,100000,[6,4,2,4,2,4,6,2],m=n+i;if(ispseudoprime(m),c++));print(c)
2026

? n=10100010001000100001089;c=1;forstep(i=2,100000,[6,4,2,4,2,4,6,2],m=n+i;if(isprime(m),c++));print(c)
2026

I'm sure there are well known methods for sieving much more effectively.

[claugoru]

First of all thanks for your answer. I apologize for my English because I use a translator.
By safe prime I mean this 10100010001000100120893 which is a prime number.
As for the mathematical language there is not much to say. The algorithm creates a map of all prime numbers in a dimension called X.
My example on a 23-digit number is just a way to highlight that with a little more time than looking for a prime number, the algorithm finds hundreds and thousands of prime numbers.


"Pari/GP can prove such small primes in less than a millisecond even on slow hardware."


I know that 23 digits is not a big number and that it is found in less than a thousand seconds but what if I told you that you could find thousands of prime numbers in less than a thousand seconds?


Given a number N of any size and a finite dimension X, the algorithm maps this dimension using only the calculation to define whether N is prime or not.


If I want to know with absolute certainty whether a number is prime or not, must I exclude that in all the prime numbers that precede it up to its root there is no divisor that cancels its primality? correct?


how this technique is used does not matter except in order to speed up the time taken, but in the end this is the only way to confirm without doubt that the number you are looking for is a prime number


Now, I am saying that this algorithm maps all prime numbers into the X dimension and if it takes my computer 1.5 hours to find a prime number and yours takes less than a thousandth of a second, it means that you will take less than a thousandth of a second, or a little more, to find thousands of prime numbers

[claugoru]

How many digits does a complicated prime number have for you?

[VBCurtis]

Originally Posted by claugoru

If I want to know with absolute certainty whether a number is prime or not, must I exclude that in all the prime numbers that precede it up to its root there is no divisor that cancels its primality? correct?

No. That's not at all how primality tests work. What you describe is called "trial division", and is the most elementary and slowest way to prove a number prime.

You keep using the word "dimension", and you keep doing so without telling us what you think it means. Until you do so, we will continue to believe you haven't discovered anything new, and are just making up words to describe something already known.

[Dr Sardonicus]

Originally Posted by claugoru

If I want to know with absolute certainty whether a number is prime or not, must I exclude that in all the prime numbers that precede it up to its root there is no divisor that cancels its primality? correct?

No.

And before you post again, please read and study this thread, this thread, this thread, this thread, this thread, this thread, and this thread until you understand them all.

Thank you.

[xilman]

Originally Posted by claugoru

First of all thanks for your answer. I apologize for my English because I use a translator.
By safe prime I mean this 10100010001000100120893 which is a prime number.
...

I know for a fact that there are native speakers of both Italian and Portuguese on this forum.

If it helps you get your message over, please post in either (or both) languages and perhaps we may get a better translation than Google Translate can provide.