The world's unsolved problems
993 open questions across 14 fields, gathered from Wikipedia. Pick one and start thinking.
488 results in Mathematics · clear · surprise me
-
Are there infinitely many Wilson primes?
Read on Wikipedia → -
Are there infinitely many Wolstenholme primes?
Read on Wikipedia → -
Are there infinitely many Woodall primes?
Read on Wikipedia → -
Can a prime p satisfy 2^{p-1}\equiv 1\pmod{p^2} and 3^{p-1}\equiv 1\pmod{p^2} simultaneously?
Read on Wikipedia → -
Does every prime number appear in the Euclid–Mullin sequence?
Read on Wikipedia → -
What is the smallest Skewes's number?
Read on Wikipedia → -
For any given integer a > 0, are there infinitely many Lucas–Wieferich primes associated with the pair (a, −1)? (Specially, when a = 1,…
For any given integer a > 0, are there infinitely many Lucas–Wieferich primes associated with the pair (a, −1)? (Specially, when a = 1, this is the Fibonacci-Wieferich primes, and when a = 2, this is the Pell-Wieferich primes)
Read on Wikipedia → -
For any given integer a > 0, are there infinitely many primes p such that a'p − 1 ≡ 1 (mod p2)?
Read on Wikipedia → -
For any given integer b which is not a perfect power and not of the form −4k4 for integer k, are there infinitely many repunit primes to…
For any given integer b which is not a perfect power and not of the form −4k4 for integer k, are there infinitely many repunit primes to base b?
Read on Wikipedia → -
For any given integers k\geq 1, b\geq 2, c\neq 0, with 1=gcd(k, c) = 1 and 1=gcd(b, c) = 1, are there infinitely many primes of the form…
For any given integers k\geq 1, b\geq 2, c\neq 0, with 1=gcd(k, c) = 1 and 1=gcd(b, c) = 1, are there infinitely many primes of the form (k\times b^n+c)/\gcd(k+c,b-1) with integer n ≥ 1?
Read on Wikipedia → -
Is every Fermat number 2^{2^n} + 1 composite for n > 4?
Read on Wikipedia → -
Is 509,203 the lowest Riesel number?
Read on Wikipedia → -
Does the partition principle (PP) imply the axiom of choice (AC)?
Read on Wikipedia → -
(Woodin) Does the generalized continuum hypothesis below a strongly compact cardinal imply the generalized continuum hypothesis everywhere?
Read on Wikipedia → -
Does the generalized continuum hypothesis entail {\diamondsuit(E^{\lambda^+}_{\operatorname{cf}(\lambda)}}) for every singular cardinal…
Does the generalized continuum hypothesis entail {\diamondsuit(E^{\lambda^+}_{\operatorname{cf}(\lambda)}}) for every singular cardinal \lambda?
Read on Wikipedia → -
Does the generalized continuum hypothesis imply the existence of an ℵ2-Suslin tree?
Read on Wikipedia → -
If ℵω is a strong limit cardinal, is 2^{\aleph_\omega} ω4, was obtained by Shelah using his PCF theory.
Read on Wikipedia → -
The problem of finding the ultimate core model, one that contains all large cardinals.
Read on Wikipedia → -
Woodin's Ω-conjecture
if there is a proper class of Woodin cardinals, then Ω-logic satisfies an analogue of Gödel's completeness theorem.
Read on Wikipedia → -
Does the consistency of the existence of a strongly compact cardinal imply the consistent existence of a supercompact cardinal?
Read on Wikipedia → -
Does there exist a Jónsson algebra on ℵω?
Read on Wikipedia → -
Is OCA (the open coloring axiom) consistent with 2^{\aleph_{0}}>\aleph_{2}?
Read on Wikipedia → -
Reinhardt cardinals
Without assuming the axiom of choice, can a nontrivial elementary embedding V→V exist?
Read on Wikipedia → -
Baum–Connes conjecture
the assembly map is an isomorphism.
Read on Wikipedia → -
Berge conjecture that the only knots in the 3-sphere which admit lens space surgeries are Berge knots.
Read on Wikipedia → -
Bing–Borsuk conjecture
every n-dimensional homogeneous absolute neighborhood retract is a topological manifold.
Read on Wikipedia → -
Borel conjecture
aspherical and closed manifolds are determined up to homeomorphism by their fundamental groups.
Read on Wikipedia → -
Halperin conjecture on rational Serre spectral sequences of certain fibrations.
Read on Wikipedia → -
Hilbert–Smith conjecture
if a locally compact topological group has a continuous, faithful group action on a topological manifold, then the group must be a Lie group.
Read on Wikipedia → -
Mazur's conjectures
Read on Wikipedia →
Data last refreshed 2026-10-20 03:01 UTC.