Have you ever wondered how to quickly calculate the square of a number that's near a known square? There's a neat formula that can help with this, using the distance between the number you want to square and a known square. Formula Explanation: (Known square) ± {(target number) * (distance * 2) ± (distance²)} Let's break this down with some examples to make it clear: Example 1: Calculating 77² when 80² = 6400 Known square: (80² = 6400 ) Target number: ( 77)... Finding Squares Using a Known Square: A Simple Formula Explained ..read more

The answer to solving problems/general mathematics, and problems related to solving the Riemann equation can be found in the attached files. With respect and love Grigorii Anfimov ..read more

I know every prime row of pascal's triangle added up, and then subtracted by 2 has a factor of p, where p is the prime used for the prime row. Can you prove no prime rows of pascal's triangle added up and subracted by 2, ever has p^2 as a factor ..read more

Yesterday I saw on twirpx I saw an interesting article "Petrov I.B. Study of the prime number formula f(a) = a * dr(a) + 1". The article discusses a new approach to the study of prime numbers, based on the numerical roots of numbers. the prime number formula f(a) = a * dr(a) + 1 is studied, where dr(a) is the numerical root of the number a. The study shows that this formula provides a competitive probability of finding prime numbers over a wide range of values of a, appearing to be a... Formula for finding prime numbers f(a) = a * dr(a) + 1 ..read more

There is the so-called “Proteus theorem or heteroscaling theorem,” which was probably first voiced (as a separate statement) by Ib Petrov (Ib is a real name, he was surprised himself) in his article of the same name. Petrov Ib. "Proteus' Theorem or Heteroscaling Theorem", self-published, 2024. — 6 с. (publication in Russian). Actually the theorem goes like this: Theorem: For integers a, b and c, where c > 1, a > 1 and b > 1, the equations... Is Proteus' Theorem true ..read more

With precision in my inquiry, I am interested to learn whether there is any mathematical framework, method, or algorithm capable of efficiently identifying all prime numbers around a specific numerical value, such as 125,468,923, within a predetermined range of [-10,000, +10,000]. This approach would ideally bypass the exhaustive testing of every candidate within this interval, utilizing a more strategic mechanism for isolating and confirming primes. Insights into such methods are earnestly... Seeking Efficient Prime Identification Methods for Constrained Numerical Ranges ..read more

105840792690619648459681960002881 126840792690619648459681960002881 131840792690619648459681960002881 135840792690619648459681960002881 231840792690619648459681960002881 288840792690619648459681960002881 296840792690619648459681960002881 324840792690619648459681960002881 356840792690619648459681960002881 363840792690619648459681960002881 380840792690619648459681960002881 399840792690619648459681960002881 425840792690619648459681960002881 434840792690619648459681960002881 Execution time:... Innovating Primes: How the Prime Heart Theorem Could Change Everything ..read more

CHAT GTP1+2+4+8+16+32+5063+10126+20252+40504+81008=162496.1+2+4+8+16+32+5063+10126+20252+40504+81008=162496.Since the sum does indeed equal 162496, based on this calculation, it supports the claim that 162496 is a perfect number ..read more

Let's call a number N 'sub-perfect' if the sum of its divisors less than N is N-1. (There may be a different term for such numbers). It is easy to see that powers of 2 are sub-perfect. Does anyone know a proof or counter-example to the conjecture that all sub-perfect numbers are powers of 2 ..read more

I am sorry for my English. 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... Is Petrov’s “metaremultion” finite ..read more