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Unsolved problems in mathematics

This article lists some [unsolved problems] in [mathematics] . See individual articles for details and sources.

Millennium Prize Problems
Of the seven [Millennium Prize Problems] set by the [Clay Mathematics Institute] , the six yet to be solved are:
- [P versus NP]
- The [Hodge conjecture]
- The [Riemann hypothesis]
- [Yang–Mills existence and mass gap]
- [Navier-Stokes existence and smoothness]
- The [Birch and Swinnerton-Dyer conjecture] .
Only the [Poincaré conjecture] has been solved. The smooth four dimensional [Poincaré conjecture] is still unsolved. That is, can a four dimensional topological sphere have two or more inequivalent [smooth structure] s?

Other still-unsolved problems
Additive number theory
- [Goldbach's conjecture] and its [weak version]
- The values of g(k) and G(k) in [Waring's problem]
- [Collatz conjecture] (3n 1 conjecture)
- [Gilbreath's conjecture]

Number theory: prime numbers
- [Catalan's Mersenne conjecture]
- [Twin prime conjecture]
- Are there infinitely many [prime quadruplet] s?
- Are there infinitely many [Mersenne prime] s ( [Lenstra-Pomerance-Wagstaff conjecture] ); equivalently, infinitely many even [perfect number] s?
- Are there infinitely many [Sophie Germain prime] s?
- Are there infinitely many [regular prime] s, and if so is their relative density e^{-1/2}?
- Are there infinitely many [Cullen prime] s?
- Are there infinitely many [palindromic prime] s in base 10?
- Are there infinitely many [Fibonacci prime] s?
- Is every [Fermat number] 22 n 1 composite for n > 4?
- Is 78,557 the lowest [Sierpinski number] ?
- Is 509,203 the lowest [Riesel number] ?
- [Fortune's conjecture] (that no [Fortunate number] is composite)
- [Polignac's conjecture]
- [Landau's problems]

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