Finding prime numbers using the "Petrov method"?

[syndicatel]

I am sorry for my English.

There is such an alternative (in every sense) mathematician I.B. Petrov, but sometimes in his publications you can find very interesting thoughts and ideas (which other authors do not have). From the latest publication “Petrov I.B. Interesting binary epistemomatic statement about some prime numbers as a possible basis for a new sequence for their search., 2023, SI”:

I won’t cite the author’s statements - it’s really confusingly written there, but the meaning is something like this: if you take some prime numbers and do it like this, for example the number 37; (3^2.3)x(7^6.7)=5748251.4024... That is the integer part, that is, the number 5748251 is prime.

Well, that is, I think the idea is clear. The devil knows how the good gentleman came up with this idea (I really didn’t understand the logic and wouldn’t have gotten to this point even on hallucinogens ), but he probably invented it all for a reason. Unfortunately, in addition to the statement, there are only other interesting things there for the numbers 2777 and 7727, Near-Repdigit (damn, well, they’ll come up with designs with prefixes :shock, but these are all particulars. Unfortunately, nothing more has been written.

I was thinking, what if I made a program in C# that runs all the prime numbers through a list (any kind) using this formula. Maybe something good will come out? It's just a little more complicated than with natural indicators. I don’t understand, is this purely the author’s fantasy or is there some deep mathematical meaning in this?

 

[blamocur]

Well, that is, I think the idea is clear.

Is it?

 

[fresh_42]

[imath] 17 [/imath] is prime and [imath] 1^{2.3}=1 \, , \,\left[7^{6.7}\right]=459,363[/imath] is divisible by [imath] 3. [/imath]
[imath] 23 [/imath] is prime and [imath] 2^{2.3} \, \cdot \,3^{6.7}= 7,746.... [/imath] is divisible by [imath] 2. [/imath]

You normally don't get very far by numerology like this. There are more fascinating equations like that, e.g. the polynomial
[math] p(n)=n^2+n+41 [/math] that spits out primes up to [imath] n=39 [/imath] or the equation
[math] 2^n+7^n+8^n+18^n+19^n+24^n=3^n+4^n+12^n+14^n+22^n+23^n .[/math] But before you start an induction, and the start is promising since it holds for [imath] n=0,1,2,3,4,5, [/imath] it fails at [imath] n=6. [/imath]

 

[syndicatel]

Thanks!

This author has another article where the number 2777 appears... In this sense, it is more interesting)))

 

[Agent Smith]

I like the overall direction Petrov is taking. I wonder if Petrov's read Gauss [imath]\pm 50[/imath] suns. I believe he has, which is good.