Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
Universal point sets for planar graphsMohar✭✭✭0Graph Theory » Topological G.T. » Drawingsmdevos
Linear Hypergraphs with Dimension 3Ossona de Mendez; Rosenstiehl; de Fraysseix✭✭0Graph Theory » Topological G.T. » Drawingstaxipom
Consecutive non-orientable embedding obstructions✭✭✭0Graph Theory » Topological G.T. » GenusBruce Richter
What is the largest graph of positive curvature?DeVos; Mohar1Graph Theory » Topological G.T. » Planar graphsmdevos
Growth of finitely presented groupsAdyan✭✭✭0Group Theorymdevos
Subgroup formed by elements of order dividing nFrobenius✭✭0Group Theorydlh12
Burnside problemBurnside✭✭✭✭0Group Theorydlh12
Inverse Galois ProblemHilbert✭✭✭✭0Group Theorytchow
Which lattices occur as intervals in subgroup lattices of finite groups?✭✭✭✭0Group Theorywilliamdemeo
F_d versus F_{d+1}Krajicek✭✭✭0Logiczitterbewegung
Tarski's exponential function problemTarski✭✭0LogicCharles
Termination of the sixth Goodstein SequenceGraham0Logicmdevos
Fixed-point logic with countingBlass✭✭0Logic » Finite Model Theorydberwanger
Order-invariant queriesSegoufin✭✭0Logic » Finite Model Theorydberwanger
Monadic second-order logic with cardinality predicatesCourcelle✭✭0Logic » Finite Model Theorydberwanger
Blatter-Specker Theorem for ternary relationsMakowsky✭✭0Logic » Finite Model Theorydberwanger
MSO alternation hierarchy over picturesGrandjean✭✭0Logic » Finite Model Theorydberwanger
Finite entailment of Positive Horn logicMartin✭✭0Logic » Finite Model TheoryLucSegoufin
Vertex Cover Integrality GapAtserias✭✭0Logic » Finite Model Theorydberwanger
Lonely runner conjectureCusick; Wills✭✭✭0Number Theorymdevos
MacEachen ConjectureMcEachen1Number Theorybillymac00
Chowla's cosine problemChowla✭✭✭0Number Theorymdevos
Quartic rationally derived polynomialsBuchholz; MacDougall✭✭✭0Number Theorymdevos
A discrete iteration related to Pierce expansionsShallit✭✭1Number Theoryshallit
Algebraic independence of pi and e✭✭✭0Number Theoryporton
Odd perfect numbersAncient/folklore✭✭✭1Number Theoryazi
Diophantine quintuple conjecture✭✭1Number Theorymaxal
Twin prime conjecture✭✭✭✭0Number Theorykaushiks.nitt
Polignac's Conjecturede Polignac✭✭✭0Number TheoryHugh Barker
Special PrimesGeorge BALAN1Number Theorymaththebalans
Primitive pythagorean n-tuple tree✭✭0Number Theorytsihonglau
3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime✭✭0Number Theoryprinceps
Erdős–Straus conjectureErdos; Straus✭✭1Number TheoryACW
Lucas Numbers Modulo m✭✭1Number TheoryMartin Erickson
Sum of prime and semiprime conjectureGeoffrey Marnell✭✭0Number Theoryprinceps
Giuga's Conjecture on PrimalityGiuseppe Giuga✭✭0Number Theoryprinceps
Alexa's Conjecture on PrimalityAlexa✭✭0Number Theoryprinceps
Birch & Swinnerton-Dyer conjecture✭✭✭✭0Number Theoryeyoong
The Erdos-Turan conjecture on additive basesErdos; Turan✭✭✭✭0Number Theory » Additive N.T.mdevos
Goldbach conjectureGoldbach✭✭✭✭0Number Theory » Additive N.T.Benschop
Are there an infinite number of lucky primes?Lazarus: Gardiner: Metropolis; Ulam1Number Theory » Additive N.T.cubola zaruka
The Riemann HypothesisRiemann✭✭✭✭0Number Theory » Analytic N.T.eric
Schanuel's ConjectureSchanuel✭✭✭✭0Number Theory » Analytic N.T.Charles
Distribution and upper bound of mimic numbersBhattacharyya✭✭1Number Theory » Analytic N.T.facility_cttb@i...
Lindelöf hypothesisLindelöf✭✭0Number Theory » Analytic N.T.porton
Euler-Mascheroni constant✭✭✭0Number Theory » Analytic N.T.Juggernaut
Is Skewes' number e^e^e^79 an integer?✭✭0Number Theory » Analytic N.T.VladimirReshetnikov
Are all Fermat Numbers square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are there only finite Fermat Primes?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
Are all Mersenne Numbers with prime exponent square-free?✭✭✭0Number Theory » Analytic N.T.kurtulmehtap
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