# conjecture

1. ### Proof of goldbach's conjecture

PROOF OF GOLDBACHâ€™S CONJECTURE Goldbachâ€™s conjecture states that every even integer > 2 is the sum of 2 primes. An example is 100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53. An alternative statement of the conjecture is as follows. Every integer > 3 is the arithmetic mean of...
2. ### conjecture

A(n) = m if 1/1 + 1/2 + 1/3 + ... + 1/(m-1) < n < 1 + 1/2 + 1/3 + ... + 1/(m) for example A(1) = 1 A(2) = 4 1/1 + 1/2 + 1/3 < 2 < 1/1 + 1/2 + 1/3 + 1/4 A(3) = 11 A(4) = 31 A(5) = 83 A(6) = 227 A(7) = 614 conjecture lim A(n+1)/A(n) = e for example A(2)/A(1) = 4 A(3)/A(2) =...
3. ### Counter to the abc Conjecture

Counter to the abcCounter to the abc C Conjecture (version 14). The abc conjecture states: 1.) max (|a|, |b|, |c|) =< C_e PROD_{p|abc} p^(1+e) for any e > 0. 2.1) C_m has an upper bound. Result (complete): 2.2) C_m has no upper bound nor limit. proof. given: 1.) max...
4. ### A Proof of Fermat's Conjecture

Hello, Welcoming myself I have a proof of Fermat's Conjecture at: https://www.dropbox.com/s/xxdtksxplf02yaj/%5B1.%20proof%20of%20Fermat%27s%20%28V17FIRM%29%20.pdf?dl=0 within my Dropbox folder at: https://www.dropbox.com/sh/gabop77dlx550wg/AADerU5lqy9yiFKkO0JOExzRa?dl=0 Also...
5. ### Proof of twin prime conjecture

PROOF OF THE TWIN PRIME CONJECTURE The twin prime conjecture states that there are an infinite number of twin primes. Twin primes are a pair of primes that differ by 2 e.g. 11 and 13, 17 and 19, 29 and 31. Consider the sieve of Eratosthenes acting on the infinite number line. 2 makes the first...
6. ### counterexamples to the Poincare conjecture

The Poincare conjecture says, "Every simply connected closed 3-manifold is homeomorphic to the 3-sphere." But there may be spaces which are simply connected closed 3-manifolds but are not homeomorphic to the Poincare conjecture. Here are some examples...
7. ### Collatz Conjecture

Hello, I am from Spain and I am asking in some forums for my ideas about Collatz Conjecture, the next text are translated by google, and I expect that you can understand me. Thank you. DRAFT: IN SEARCH OF THE DEMONSTRATION OF THE COLLATZ CONJECT I apologize if the ideas are not very clear...
8. ### Conjecture concerning a subset of Sofie-Germain primes

Conjecture: If and only if P(n) and P(n * 2 + 1) are true then n belongs to a subset of Sofie-Germain primes, where P is a boolean function defined as P(m) = { true if 2^((m +1) / 2) = -2 mod m; otherwise false }. Any idea how to disprove such a thing (or even just a counterexample)?
9. ### Proof of Beal conjecture

If $$a^x+b^y=c^z$$ for positive integers $a$, $b$, $c$, $x$, $y$ and $z$ such that $x$, $y$, $z>2$ then $a$, $b$ and $c$ have a common prime factor. Proof Let $a=ue$, $b=uf$ and $c=ug$ such that $u$, $e$, $f$ and $g$ are positive integers. \begin{align*} (ue)^x+(uf)^y&=(ug)^z\\...
10. ### Proof of Legendre's conjecture

Hi Guys, I'd like to share with you my proof of Legendre's conjecture, that there is always a prime between n^2 and (n+1)^2. It's very simple and intuitive - based on my idea of patterns of divisibility of numbers. What do you think about it? :-) https://youtu.be/Q4qpsdNugFk Marcin
11. ### Semi-prime factorization conjecture

Let N be a semiprimo then N=a^2-b^2 will have two solutions a1=(N+1)/2 and b1=(N-1)/2 a2=? b2=? bruteforce on b2 starting from 0 A+B=a1 , A-B=a2 , C+D=b1 ,C-D=b2 gcd(A,C)=p_a gcd(B,D)=p_b p=(p_a^2-p_b^2) gcd(A,D)=q_a gcd(B,C)=q_b q=(q_b^2-q_a^2) Example 15=a^2-b^2...
12. ### Collatz Conjecture Unrevised Proof Attempt

https://scribd.com/document/364439993 Please help me find an error in this proof attempt of the notorious Collatz Conjecture. Note that the proof is unrevised and is likely to contain an error. Also, I have very little training and experience writing formal mathematics. Define any...
13. ### Collatz Conjecture Idea

Writing from a phone, so please excuse any poor formatting. So obviously with the Collatz conjecture all odd numbers don't need to be checked. That being said would it be just as hard to prove that over time all numbers put through the function have a tendency to decrease in size? I mean...
14. ### Collatz Conjecture

I was recently thinking back to the collatz conjecture and decided to just think about it for a while. For those who do not know, the conjecture is basically this: If n is even divide n by 2. If n is odd, multiply n by three then add one. Take that answer and repeat the process such that you...
15. ### Ulam's packing conjecture with spheres

â€œ(Packed) identical balls must leave (a maximum of) ~25.95% of the space empty." [Wikipedia] Is there a maximum curvature for the average, asymmetric packing of spheres in 3D space? In the 2D case, maximally packed circles can go on countlessly with zero curvature in six directions.
16. ### Lander, Parkin, and Selfridge conjecture, Proof

And finally the Lander, Parkin, and Selfridge conjecture has his proof. It involves all my previous works, and the simple concept of "free variables".... Is a boring tricky work with Sums, Linearization and Combinations, like I did for Beal, but of course is more general. I already given some...

Any factorial number n! can be written at least once as : n! = a*phi(a)*b*phi(b) phi() is the Euler totient a and b are positive integers We could note it : n!=F(a,b) Examples k! a b 1 1 1 2 1 2 3 1 3 4 2 6 5 3 5 6 3 15 7 5 21 8 20 21 9 35 36 10 70 90...
18. ### collatz conjecture - an easier way

I found an easier way to prove the Collatz conjecture. All you need to do is to prove that the minimum value of any cycle has to be above 1.5^y when y is the odd number of values in that cycle (y > 8). Way more simple then all the other stuff no?
19. ### Conjecture about odd numbers

Any odd number O >=3 could be written at least once as : O=pq - phi(pq) where p and q are both odd primes (p<=q) phi(pq) is the Euler totient of pq Example : O=3 O=3*3- phi(3*3)=9-phi(9)=9-6=3 O=7 O=3*5-phi(3*5)=15-phi(15)=15-8=7 O=5 O=25-phi(25)=5 etc... Is this...