![](/files/happy5.png)
Are there infinite number of Mersenne Primes? ★★★★
Author(s):
Conjecture A Mersenne prime is a Mersenne number
that is prime.
![\[ M_n = 2^p - 1 \]](/files/tex/eb18a56e5c2e8b1be6ac733d217c0c1f1a47a94e.png)
Are there infinite number of Mersenne Primes?
Keywords: Mersenne number; Mersenne prime
Are all Mersenne Numbers with prime exponent square-free? ★★★
Author(s):
Conjecture Are all Mersenne Numbers with prime exponent
Square free?
![$ {2^p-1} $](/files/tex/54e6687faa8a34ace9d1e2e77619c37e1e1ca30c.png)
Keywords: Mersenne number
What are hyperfuncoids isomorphic to? ★★
Author(s): Porton
Let be an indexed family of sets.
Products are for
.
Hyperfuncoids are filters on the lattice
of all finite unions of products.
Problem Is
a bijection from hyperfuncoids
to:
![$ \bigcap^{\mathsf{\tmop{FCD}}} $](/files/tex/3c8ed688fbcae181a7b030c7071347137615d338.png)
![$ \mathfrak{F} \Gamma $](/files/tex/2d4cbeff4993cf10008cbe69e72409840d1b2201.png)
- \item prestaroids on
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
![$ \mathfrak{A} $](/files/tex/702b76abd81b24daaf0e6bc2a191fb964b09d1b2.png)
If yes, is defining the inverse bijection? If not, characterize the image of the function
defined on
.
Consider also the variant of this problem with the set replaced with the set
of complements of elements of the set
.
Keywords: hyperfuncoids; multidimensional