# 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

948 questions
Filter by
Sorted by
Tagged with
87 views

### Are 2, 3 the only prime numbers that don't have the digit 1 and are palindromes whose squares are also palindromes?

While thinking about prime numbers, I noticed that: $(1)$ Very few prime numbers have squares that are palindromes. Ex: $2$, $3$, $11$, $101$, $307$ $(2)$ Even rarer are prime numbers that are ...
72 views

### Are there infinitely many solutions such that the digit sum of a prime power is a smaller power of the same prime?

While discussing prime powers and divisors, I came up with the following problem. Examples $\to$ prime $p=3$ digit sum (in base ten) of $p^3=27$ is $p^2=9$, a power of $p$,. $\to$ prime $p=7$ ...
104 views

### Minimal order of a counterexample to Wall’s conjecture

There used to be once a rather well known and interesting conjecture, that was formulated by Gordon E. Wall: The number of maximal subgroups of a finite group $G$ does not exceed $|G|$ That ...