# Questions tagged [conjectures]

For questions related to conjectures which are suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found

949 questions
Filter by
Sorted by
Tagged with
160 views

### Question regarding the status of Erdős' conjectures

Has Erdős' conjecture on arithmetic progressions or his conjecture on Sylvester's sequence been proven?
4k views

### Which notable mathematicans have tried solving the Riemann hypothesis?

I have read that the Riemann hypothesis is the most important open question in mathematics and has been open since 1859. I am wondering which famous mathematicians have actually tried to solve it and ...
233 views

### On expressing a square as a sum of two cubes

Given $a,b,c \in \mathbb{N}$ which satisfy the following conditions: $a^3 + b^3 = c^2$ $a \neq b$ =-=-=-=-=-=-=-=-=-=-=-=-=-= EDIT, Will Jagy: The conjecture is that, for a given $c,$ there are at ...
4k views

### Why is Goldbach's conjecture not included in the millenium prize problems

As we all know, the Goldbach's Conjecture is one one of the oldest and best-known unsolved problems in mathematics. I was going through some of the attempts made to solve it and got fascinated as to ...
95 views

### Prime clasfication by some constructive function

How to prove or justify the following: $$f(g)= \frac1{1-g^2} \prod_{k=1}^{\infty} \left(\frac{\sin(\pi \frac gk)}{\pi \frac gk} \cdot \frac 1{1-\frac{g^2}{k^2}}\right).$$ The above statement can ...
259 views

### Goldbach conjecture and primes

I need some clarification on (1) Is there any proof to say Mersenne primes $M_p$ are finite or infinite? if there, could you share here.. (2) If Goldbach is conjecture is true, how you can justify the ...
2k views

### Fibonacci conjecture: $(F_{n+5})^2 - (F_n)^2 = 3((F_{n+3})^2 - (F_{n+2})^2) + 8 F_{n+2} F_{n+3}$.

So this is the question I have The Fibonacci sequence is a recurrence system given by $$F_1 = 1, \ F_2 = 1, \ F_{n+2} = F_{n+1} + F_n \qquad (n = 1, 2, 3, \ldots).$$ This question concerns the ...
194 views

### Primes + Inetvel + conjecture on primes

a) Can we establish a proof, there exists infinitely many primes of the form $n^2$ + 1. Why is the unit digit of such a prime p always 1 or 7? Is there any reasonable procedure or concept for the fact ...
8k views

### Does giving a counterexample to a conjecture prove it to be true or false?

If a problem asks me to give a counterexample to a conjecture, am I proving the conjecture true or false by giving a counterexample? I am leening towards proving it false, because if I were to prove ...
321 views

### Has every finite group a minimal presentation?

For a finite group $G$ let $d(G)$ be the minimal number of generators of $G$ and let $r(G)$ be the minimal number such that $G$ has a finite presentation with $r(G)$ relators. Call a presentation with ...
553 views

### Asymptotic FLT $\implies$FLT using ABC Conjecture

Edit: I'm beginning to suspect I either misread the sources or perhaps something wasn't stated, but it's my guess now that there is no nontrivial way of showing the ABC conjecture implies Fermat's ...
312 views

820 views

379 views

### Does this $\zeta(s)$ identity have a name?

I have generalized the product from this thread: Let $s=2n+1$ for $n\ge1$, $$\zeta (s)=\frac{\zeta (2 s)}{\zeta (2)} \prod _{n=1}^{\infty } \frac{\sum _{i=0}^{s-1}(-p_n){}^i}{(p_{n}-1)p_{n}^{s-2}}$$ ...
635 views

### Is it known or new? [duplicate]

Possible Duplicate: Starting digits of 2^n While I was randomly working with number patterns, I came along with some interesting pattern which seems to turn to a conjecture in fact. My ...
122 views

### I noticed a pattern, does this have a name?

First of all I am a programmer, not a mathematician, so I may articulate what I am trying to say very poorly. I was working with powers of $2$ when I noticed a relationship I had never noticed before. ...
3k views

4k views

### Proving a known zero of the Riemann Zeta has real part exactly 1/2

Much effort has been expended on a famous unsolved problem about the Riemann Zeta function $\zeta(s)$. Not surprisingly, it's called the Riemann hypothesis, which asserts:  \zeta(s) = 0 \...