Questions tagged [conjectures]
for question related to conjectures.
226 questions
-4
votes
1
answer
191
views
A conjecture on prime distribution (PKD Conjecture) [closed]
I would like to propose the following conjecture
The PKD Conjecture (PKD)
Let $p,d$ be positive integers with $\gcd(p,d)=1$. There exists a function
$$
f:\mathbb{N}\to\mathbb{N}, \quad f(N)<N,
$$
...
- 23
6
votes
0
answers
190
views
Stolz conjecture
I am wondering about current status of Stolz conjecture (about vanishing of Witten genus for certain manifolds).
In which cases has it already been proven?
Thanks a lot
- 231
3
votes
0
answers
344
views
Minimizing an expression with sum of digits
Conjecture. If $S_b(n)$ denotes the sum of digits of $n$ with base $b$ then $$10 \cdot S_5(n)+12 \cdot S_2(n)-5 \cdot S_3(n) \geq 0$$ and the equality holds if and only if $n = 19925000$.
The ...
- 161
-5
votes
1
answer
272
views
Known examples of conjectures stated while suspected false, to invite counterexamples?
Sometimes, in computational or experimental mathematics, one faces statements that seem almost certainly false yet are not directly refutable by current methods or feasible computation.
In such cases, ...
- 1,965
30
votes
5
answers
2k
views
How can referees verify computationally intensive results when HPC resources are required?
This question is somewhat related to my previous question and is also inspired from this other question concerning the credibility of extensive computations (although from a different perspective).
In ...
- 1,359
12
votes
1
answer
952
views
How to share algorithms for testing a conjecture?
I am preparing a paper where some results involve computational verification of a conjecture. Of course, I am not proving the conjecture in full, but I verify it for some large values of the involved ...
- 1,359
40
votes
10
answers
4k
views
Which pairs of mutually contradicting conjectures are there?
Years ago I had the pleasure of witnessing Simon Thomas giving a wonderful talk about Martin's conjecture, which I just now fondly remembered reading this question. Even though I am not well-versed in ...
3
votes
0
answers
138
views
Conjectures of Ext (non)-vanishing for noetherian rings
I am interested in a collection of open problems or conjectures on Ext (non)-vanishing results for modules over noetherian rings.
Here some examples:
Modular representation theory
Let $G$ be a finite ...
- 28.1k
-3
votes
2
answers
688
views
Primality test using the Golden Ratio [closed]
Background and Motivation
The golden ratio,
$$
\phi = \frac{1 + \sqrt{5}}{2},
$$
is a well-known irrational constant that appears frequently in geometry, algebra, and in the Fibonacci and Lucas ...
- 559
1
vote
2
answers
509
views
The strong Mersenne conjecture
The strong twin conjecture:
For every number $a≥0$, there exist two prime numbers $p$ and $p+2$ such that $$a+4<p<2^{a+4}$$
and it was believed that this conjecture implies the twin conjecture.
...
- 1,265
1
vote
1
answer
292
views
Reference request: Open problems about finite free products of finite groups
I'm working with finite free products of finite groups, i.e. a group $G$ given by $$G = F_1 \ast \ldots \ast F_n$$ where each $F_i$ is finite.
Do you know of any open problems as well as references ...
11
votes
1
answer
2k
views
Why is Erdős' conjecture on arithmetic progressions not discussed much, and is there an active pathway to its resolution?
Erdős' conjecture on arithmetic progressions (also known as the Erdős–Turán conjecture) is a major open problem in arithmetic combinatorics. It asserts that if the sum of the reciprocals of the ...
- 147
3
votes
0
answers
101
views
Conjecture on the preservation of unfragmented sets under element addition
A set $A_k$ contains $k$ elements $a_i, i=1..k$. The $a_i$ are incomparable (For example, functions, matrices, etc. they cannot be connected using > or <), but an operation $\otimes$ can be ...
- 39
7
votes
0
answers
249
views
Conjectures on Smith Normal Form for Jucys-Murphy elements (Stanley, Grinberg) - status and generalisations?
There is an excellent review by R.Stanley "Smith Normal Form in Combinatorics" from 2016. At the very last page - certain conjectures on SMF (Smith Normal Form) of Jucys–Murphy elements are ...
- 26.3k
0
votes
1
answer
120
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Conjecture on a cyclic quadrilateral associated with central line of triangle
Using computer I found a conjecture as follows (click to check by geogebra):
Conjecture: Let $A$, $B$, $C$, $D$ lie on a circle such that $A$, $B$, $C$, $D$ are not formed an Isosceles trapezoid. ...
- 2,148