Conjectures.io

ProveArtin Primitive Roots Conjecture - part iNumber theory0 α

a

DisproveArtin Primitive Roots Conjecture - part iNumber theory0 α

a

ProveBorsuk Conjecture - fourConvex and discrete geometry0 α

4

DisproveBorsuk Conjecture - fourConvex and discrete geometry0 α

4

ProveBrocard ConjectureNumber theory0 α

**Brocard's Conjecture** For every n \geq 2, between the squares of the n -th and (n+1) -th primes, there are at least four\dots

DisproveBrocard ConjectureNumber theory0 α

**Brocard's Conjecture** For every n \geq 2, between the squares of the n -th and (n+1) -th primes, there are at least four\dots

ProveBunyakovskyNumber theory0 α

f

DisproveBunyakovskyNumber theory0 α

f

ProveCarmichael Totient - charmichael TotientNumber theory0 α

n

DisproveCarmichael Totient - charmichael TotientNumber theory0 α

n

ProveClass Number ProblemNumber theory0 α

There are infinitely many real quadratic fields ℚ(\sqrtd) with class number one, where d > 1 is a squarefree integer.

DisproveClass Number ProblemNumber theory0 α

There are infinitely many real quadratic fields ℚ(\sqrtd) with class number one, where d > 1 is a squarefree integer.

ProveDicksonNumber theory0 α

f_i(n) = a_i n+b_i

DisproveDicksonNumber theory0 α

f_i(n) = a_i n+b_i

ProveErdős problem 10Combinatorics0 α

k

DisproveErdős problem 10Combinatorics0 α

k

ProveErdős problem 100Convex and discrete geometry0 α

A

DisproveErdős problem 100Convex and discrete geometry0 α

A

ProveErdős problem 1003Number theory0 α

\phi(n) = \phi(n+1)

DisproveErdős problem 1003Number theory0 α

\phi(n) = \phi(n+1)

ProveErdős problem 1004Number theory0 α

For any fixed c > 0, if x is sufficiently large then there exists n \leq x such that the values of φ(n+k) are all distinct for 1 \leq k\dots

DisproveErdős problem 1004Number theory0 α

For any fixed c > 0, if x is sufficiently large then there exists n \leq x such that the values of φ(n+k) are all distinct for 1 \leq k\dots

ProveErdős problem 1049Number theory0 α

t>1

DisproveErdős problem 1049Number theory0 α

t>1

ProveErdős problem 1056Number theory0 α

k ≥ 2

DisproveErdős problem 1056Number theory0 α

k ≥ 2

ProveErdős problem 1057Number theory0 α

C(x)=x^{1-o(1)}

DisproveErdős problem 1057Number theory0 α

C(x)=x^{1-o(1)}

ProveErdős problem 1060 - part iiNumber theory0 α

k \le n

DisproveErdős problem 1060 - part iiNumber theory0 α

k \le n

ProveErdős problem 1062 - part iiNumber theory0 α

Erdős asked whether the limiting density f n / n exists and, if so, whether it is irrational.

DisproveErdős problem 1062 - part iiNumber theory0 α

Erdős asked whether the limiting density f n / n exists and, if so, whether it is irrational.

ProveErdős problem 1068Combinatorics0 α

\aleph_1

DisproveErdős problem 1068Combinatorics0 α

\aleph_1

ProveErdős problem 107Convex and discrete geometry0 α

f(n)

DisproveErdős problem 107Convex and discrete geometry0 α

f(n)

ProveErdős problem 1072 - part iNumber theory0 α

p

DisproveErdős problem 1072 - part iNumber theory0 α

p

ProveErdős problem 1072 - part iiNumber theory0 α

f(p)/p \to 0

DisproveErdős problem 1072 - part iiNumber theory0 α

f(p)/p \to 0

ProveErdős problem 1073Number theory0 α

A(x) \le x^{o(1)}

DisproveErdős problem 1073Number theory0 α

A(x) \le x^{o(1)}

ProveErdős problem 1074 - EHS Numbers one halfNumber theory0 α

2^{10}

DisproveErdős problem 1074 - EHS Numbers one halfNumber theory0 α

2^{10}

ProveErdős problem 108Combinatorics0 α

For every r \geq 4 and k \geq 2 is there some finite f(k,r) such that every graph of chromatic number \geq f(k,r) contains a subgraph of\dots

DisproveErdős problem 108Combinatorics0 α

For every r \geq 4 and k \geq 2 is there some finite f(k,r) such that every graph of chromatic number \geq f(k,r) contains a subgraph of\dots

ProveErdős problem 1082 - part iGeometry0 α

A\subset \mathbb{R}^2

DisproveErdős problem 1082 - part iGeometry0 α

A\subset \mathbb{R}^2

ProveErdős problem 1085 - upper d 3Convex and discrete geometry0 α

n^{4/3}\log\log n

DisproveErdős problem 1085 - upper d 3Convex and discrete geometry0 α

n^{4/3}\log\log n

ProveErdős problem 1094Number theory0 α

n\ge 2k

DisproveErdős problem 1094Number theory0 α

n\ge 2k

ProveErdős problem 1095 - log is ThetaNumber theory0 α

\log g(k) \asymp \frac{k}{\log k}

DisproveErdős problem 1095 - log is ThetaNumber theory0 α

\log g(k) \asymp \frac{k}{\log k}

ProveErdős problem 1095 - lower conjectureNumber theory0 α

g(k)\geq\exp(c\frac{k}{\log k})

DisproveErdős problem 1095 - lower conjectureNumber theory0 α

g(k)\geq\exp(c\frac{k}{\log k})

ProveErdős problem 11Number theory0 α

n > 1

DisproveErdős problem 11Number theory0 α

n > 1

ProveErdős problem 1101 - part iNumber theory0 α

1. Is there a good sequence with polynomial growth?

DisproveErdős problem 1101 - part iNumber theory0 α

1. Is there a good sequence with polynomial growth?

ProveErdős problem 1106 - part iiNumber theory0 α

p(n)

DisproveErdős problem 1106 - part iiNumber theory0 α

p(n)

ProveErdős problem 1107Number theory0 α

r \ge 2

DisproveErdős problem 1107Number theory0 α

r \ge 2

ProveErdős problem 1108 - part iNumber theory0 α

k \geq 2

DisproveErdős problem 1108 - part iNumber theory0 α

k \geq 2

ProveErdős problem 1113 - filaseta finch kozekNumber theory0 α

**Filaseta-Finch-Kozek conjecture (2008).** Every Sierpiński number is either a perfect power or possesses a finite covering set\dots

DisproveErdős problem 1113 - filaseta finch kozekNumber theory0 α

**Filaseta-Finch-Kozek conjecture (2008).** Every Sierpiński number is either a perfect power or possesses a finite covering set\dots

ProveErdős problem 1135Number theory0 α

n

DisproveErdős problem 1135Number theory0 α

n

ProveErdős problem 1137Number theory0 α

d_n=p_{n+1}-p_n

DisproveErdős problem 1137Number theory0 α

d_n=p_{n+1}-p_n

ProveErdős problem 1142Number theory0 α

n > 2

DisproveErdős problem 1142Number theory0 α

n > 2

ProveErdős problem 1175Combinatorics0 α

\kappa

DisproveErdős problem 1175Combinatorics0 α

\kappa

ProveErdős problem 1192Combinatorics0 α

r\geq 2

DisproveErdős problem 1192Combinatorics0 α

r\geq 2

ProveErdős problem 120Combinatorics0 α

A \subseteq \mathbb{R}

DisproveErdős problem 120Combinatorics0 α

A \subseteq \mathbb{R}

ProveErdős problem 1203Number theory0 α

F(n)\to \infty

DisproveErdős problem 1203Number theory0 α

F(n)\to \infty

ProveErdős problem 1209 - part iii dNumber theory0 α

n

DisproveErdős problem 1209 - part iii dNumber theory0 α

n

ProveErdős problem 124 - ne zeroNumber theory0 α

k \ne 0

DisproveErdős problem 124 - ne zeroNumber theory0 α

k \ne 0

ProveErdős problem 126 - is Little ONumber theory0 α

f(n) = o(\frac{n}{\log n})

DisproveErdős problem 126 - is Little ONumber theory0 α

f(n) = o(\frac{n}{\log n})

ProveErdős problem 128Combinatorics0 α

n/2

DisproveErdős problem 128Combinatorics0 α

n/2

ProveErdős problem 137 - multiple powerful factorsNumber theory0 α

k

DisproveErdős problem 137 - multiple powerful factorsNumber theory0 α

k

ProveErdős problem 138Number theory0 α

\lim_{k \to \infty} (W(k))^{1/k} = \infty

DisproveErdős problem 138Number theory0 α

\lim_{k \to \infty} (W(k))^{1/k} = \infty

ProveErdős problem 14 - part iNumber theory0 α

A ⊆ \mathbb{N}

DisproveErdős problem 14 - part iNumber theory0 α

A ⊆ \mathbb{N}

ProveErdős problem 14 - part iiNumber theory0 α

|\{1,\ldots,N\} \setminus B| = o(N^\frac{1}{2})

DisproveErdős problem 14 - part iiNumber theory0 α

|\{1,\ldots,N\} \setminus B| = o(N^\frac{1}{2})

ProveErdős problem 141 - elevenCombinatorics0 α

11

DisproveErdős problem 141 - elevenCombinatorics0 α

11

ProveErdős problem 142 - lowerNumber theory0 α

r_k(N) = o_k(N / \log N)

DisproveErdős problem 142 - lowerNumber theory0 α

r_k(N) = o_k(N / \log N)

ProveErdős problem 143 - part iiNumber theory0 α

\sum_{x \in A} \frac{1}{x \log x} < \infty,

DisproveErdős problem 143 - part iiNumber theory0 α

\sum_{x \in A} \frac{1}{x \log x} < \infty,

ProveErdős problem 145Number theory0 α

s_1 < s_2 < \cdots

DisproveErdős problem 145Number theory0 α

s_1 < s_2 < \cdots

ProveErdős problem 153Combinatorics0 α

A

DisproveErdős problem 153Combinatorics0 α

A

ProveErdős problem 155Combinatorics0 α

k \geq 1

DisproveErdős problem 155Combinatorics0 α

k \geq 1

ProveErdős problem 156Combinatorics0 α

A\subset \{1,\ldots,N\}

DisproveErdős problem 156Combinatorics0 α

A\subset \{1,\ldots,N\}

ProveErdős problem 158Combinatorics0 α

Let A be an infinite B₂[2] set. Must liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0?

DisproveErdős problem 158Combinatorics0 α

Let A be an infinite B₂[2] set. Must liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0?

ProveErdős problem 168 - part iiCombinatorics0 α

F(N)/N

DisproveErdős problem 168 - part iiCombinatorics0 α

F(N)/N

ProveErdős problem 17Number theory0 α

**Erdős Problem 17.** Are there infinitely many cluster primes?

DisproveErdős problem 17Number theory0 α

**Erdős Problem 17.** Are there infinitely many cluster primes?

ProveErdős problem 172Combinatorics0 α

\mathbb{N}

DisproveErdős problem 172Combinatorics0 α

\mathbb{N}

ProveErdős problem 18 - bNumber theory0 α

h(n!) < n^{o(1)}

DisproveErdős problem 18 - bNumber theory0 α

h(n!) < n^{o(1)}

ProveErdős problem 184Combinatorics0 α

n

DisproveErdős problem 184Combinatorics0 α

n

ProveErdős problem 200Combinatorics0 α

\{1,\ldots,N\}

DisproveErdős problem 200Combinatorics0 α

\{1,\ldots,N\}

ProveErdős problem 208 - log boundNumber theory0 α

s_{n+1} - s_n \ll \log s_n

DisproveErdős problem 208 - log boundNumber theory0 α

s_{n+1} - s_n \ll \log s_n

ProveErdős problem 212Convex and discrete geometry0 α

Is there a dense subset of ℝ^2 such that all pairwise distances are rational?

DisproveErdős problem 212Convex and discrete geometry0 α

Is there a dense subset of ℝ^2 such that all pairwise distances are rational?

ProveErdős problem 213Convex and discrete geometry0 α

n \geq 4

DisproveErdős problem 213Convex and discrete geometry0 α

n \geq 4

ProveErdős problem 218 - geNumber theory0 α

n

DisproveErdős problem 218 - geNumber theory0 α

n

ProveErdős problem 218 - infinite equal prime gapNumber theory0 α

n

DisproveErdős problem 218 - infinite equal prime gapNumber theory0 α

n

ProveErdős problem 218 - leNumber theory0 α

n

DisproveErdős problem 218 - leNumber theory0 α

n

ProveErdős problem 23Combinatorics0 α

5n

DisproveErdős problem 23Combinatorics0 α

5n

ProveErdős problem 233Number theory0 α

N

DisproveErdős problem 233Number theory0 α

N

ProveErdős problem 234Number theory0 α

Is it true that for all c \geq 0, the density f c of integers for which (p (n + 1) - p n) / log n < c exists and is a\dots

DisproveErdős problem 234Number theory0 α

Is it true that for all c \geq 0, the density f c of integers for which (p (n + 1) - p n) / log n < c exists and is a\dots

ProveErdős problem 236Combinatorics0 α

f(n)

DisproveErdős problem 236Combinatorics0 α

f(n)

ProveErdős problem 238Number theory0 α

Let c₁, c₂ > 0 . Is it true that for any sufficiently large x, there exists more than c₁ * log x many consecutive primes\dots

DisproveErdős problem 238Number theory0 α

Let c₁, c₂ > 0 . Is it true that for any sufficiently large x, there exists more than c₁ * log x many consecutive primes\dots

ProveErdős problem 241 - generalizationCombinatorics0 α

A\subseteq \{1,\ldots,N\}

DisproveErdős problem 241 - generalizationCombinatorics0 α

A\subseteq \{1,\ldots,N\}

ProveErdős problem 242 - schinzel generalizationNumber theory0 α

a

DisproveErdős problem 242 - schinzel generalizationNumber theory0 α

a

ProveErdős problem 243Sequences and series0 α

a_1 < a_2 < \dots

DisproveErdős problem 243Sequences and series0 α

a_1 < a_2 < \dots

ProveErdős problem 244Number theory0 α

C > 1

DisproveErdős problem 244Number theory0 α

C > 1

ProveErdős problem 247Number theory0 α

n_1 < n_2 < \cdots

DisproveErdős problem 247Number theory0 α

n_1 < n_2 < \cdots

ProveErdős problem 249Number theory0 α

\sum_{n} \frac{\phi(n)}{2^n}

DisproveErdős problem 249Number theory0 α

\sum_{n} \frac{\phi(n)}{2^n}

ProveErdős problem 25Number theory0 α

n_1 < n_2 < \dots

DisproveErdős problem 25Number theory0 α

n_1 < n_2 < \dots

ProveErdős problem 251Number theory0 α

\sum_{n=1}^\infty \frac{p_n}{2^n}

DisproveErdős problem 251Number theory0 α

\sum_{n=1}^\infty \frac{p_n}{2^n}

ProveErdős problem 252Number theory0 α

k

DisproveErdős problem 252Number theory0 α

k

ProveErdős problem 257Number theory0 α

A\subseteq\mathbb{N}

DisproveErdős problem 257Number theory0 α

A\subseteq\mathbb{N}

ProveErdős problem 263 - part iNumber theory0 α

a_n = 2^{2^n}

DisproveErdős problem 263 - part iNumber theory0 α

a_n = 2^{2^n}

ProveErdős problem 264 - part iiNumber theory0 α

n!

DisproveErdős problem 264 - part iiNumber theory0 α

n!

ProveErdős problem 269 - irrationalNumber theory0 α

P

DisproveErdős problem 269 - irrationalNumber theory0 α

P

ProveErdős problem 274 - herzog schonheimGroup theory0 α

G

DisproveErdős problem 274 - herzog schonheimGroup theory0 α

G

ProveErdős problem 28Number theory0 α

A ⊆ \mathbb{N}

DisproveErdős problem 28Number theory0 α

A ⊆ \mathbb{N}

ProveErdős problem 282Combinatorics0 α

A\subseteq \mathbb{N}

DisproveErdős problem 282Combinatorics0 α

A\subseteq \mathbb{N}

ProveErdős problem 287Number theory0 α

k\geq2

DisproveErdős problem 287Number theory0 α

k\geq2

ProveErdős problem 291 - part iNumber theory0 α

n\geq 1

DisproveErdős problem 291 - part iNumber theory0 α

n\geq 1

ProveErdős problem 291 - shiu heuristic density zeroNumber theory0 α

n

DisproveErdős problem 291 - shiu heuristic density zeroNumber theory0 α

n

ProveErdős problem 3Number theory0 α

A \subset \mathbb{N}

DisproveErdős problem 3Number theory0 α

A \subset \mathbb{N}

ProveErdős problem 30Number theory0 α

\varepsilon > 0

DisproveErdős problem 30Number theory0 α

\varepsilon > 0

ProveErdős problem 304 - upper boundNumber theory0 α

N(b) \ll \log \log b

DisproveErdős problem 304 - upper boundNumber theory0 α

N(b) \ll \log \log b

ProveErdős problem 307Number theory0 α

P

DisproveErdős problem 307Number theory0 α

P

ProveErdős problem 313 - primary pseudoperfect are infiniteNumber theory0 α

It is conjectured that the set of primary pseudoperfect numbers is infinite.

DisproveErdős problem 313 - primary pseudoperfect are infiniteNumber theory0 α

It is conjectured that the set of primary pseudoperfect numbers is infinite.

ProveErdős problem 317 - claim 2Number theory0 α

n

DisproveErdős problem 317 - claim 2Number theory0 α

n

ProveErdős problem 32Number theory0 α

A \subseteq \mathbb{N}

DisproveErdős problem 32Number theory0 α

A \subseteq \mathbb{N}

ProveErdős problem 323 - part iNumber theory0 α

f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}

DisproveErdős problem 323 - part iNumber theory0 α

f_{k,k}(x) \gg_\epsilon x^{1-\epsilon}

ProveErdős problem 323 - part iiNumber theory0 α

m < k

DisproveErdős problem 323 - part iiNumber theory0 α

m < k

ProveErdős problem 323 - k gt 2Number theory0 α

k>2

DisproveErdős problem 323 - k gt 2Number theory0 α

k>2

ProveErdős problem 324 - quinticNumber theory0 α

f(x) = x^5

DisproveErdős problem 324 - quinticNumber theory0 α

f(x) = x^5

ProveErdős problem 325Number theory0 α

f_{k, 3}(x)

DisproveErdős problem 325Number theory0 α

f_{k, 3}(x)

ProveErdős problem 340Combinatorics0 α

A = \{1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, \ldots\}

DisproveErdős problem 340Combinatorics0 α

A = \{1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, \ldots\}

ProveErdős problem 340 - sub has Pos DensityCombinatorics0 α

A - A

DisproveErdős problem 340 - sub has Pos DensityCombinatorics0 α

A - A

ProveErdős problem 354 - part iNumber theory0 α

\alpha,\beta\in \mathbb{R}_{>0}

DisproveErdős problem 354 - part iNumber theory0 α

\alpha,\beta\in \mathbb{R}_{>0}

ProveErdős problem 357 - part iNumber theory0 α

f(n)

DisproveErdős problem 357 - part iNumber theory0 α

f(n)

ProveErdős problem 357 - infinite set densityNumber theory0 α

A

DisproveErdős problem 357 - infinite set densityNumber theory0 α

A

ProveErdős problem 357 - infinite set sumNumber theory0 α

A

DisproveErdős problem 357 - infinite set sumNumber theory0 α

A

ProveErdős problem 357 - monotone, part iNumber theory0 α

h(n)

DisproveErdős problem 357 - monotone, part iNumber theory0 α

h(n)

ProveErdős problem 359 - part iNumber theory0 α

a_1< a_2 < ⋯

DisproveErdős problem 359 - part iNumber theory0 α

a_1< a_2 < ⋯

ProveErdős problem 359 - part iiNumber theory0 α

a_1< a_2 < ⋯

DisproveErdős problem 359 - part iiNumber theory0 α

a_1< a_2 < ⋯

ProveErdős problem 359 - is Good For 1 asymptoticNumber theory0 α

A

DisproveErdős problem 359 - is Good For 1 asymptoticNumber theory0 α

A

ProveErdős problem 364Number theory0 α

There is no consecutive triple of powerful numbers.

DisproveErdős problem 364Number theory0 α

There is no consecutive triple of powerful numbers.

ProveErdős problem 364 - strongNumber theory0 α

n_k

DisproveErdős problem 364 - strongNumber theory0 α

n_k

ProveErdős problem 366Number theory0 α

2

DisproveErdős problem 366Number theory0 α

2

ProveErdős problem 371Number theory0 α

P(n)

DisproveErdős problem 371Number theory0 α

P(n)

ProveErdős problem 373Number theory0 α

Show that the equation n!=a_1!a_2!\cdot\cdot\cdota_k!, with n-1 > a_1 \geq a_2 \geq \cdot\cdot\cdot \geq a_k, has only finitely many solutions.

DisproveErdős problem 373Number theory0 α

Show that the equation n!=a_1!a_2!\cdot\cdot\cdota_k!, with n-1 > a_1 \geq a_2 \geq \cdot\cdot\cdot \geq a_k, has only finitely many solutions.

ProveErdős problem 373 - maximal solutionNumber theory0 α

Hickerson conjectured the largest solution the equation n!=a_1!a_2!\cdot\cdot\cdota_k!, with n-1 > a_1 \geq a_2 \geq \cdot\cdot\cdot \geq a_k, is 16!=14!5!2! \dots

DisproveErdős problem 373 - maximal solutionNumber theory0 α

Hickerson conjectured the largest solution the equation n!=a_1!a_2!\cdot\cdot\cdota_k!, with n-1 > a_1 \geq a_2 \geq \cdot\cdot\cdot \geq a_k, is 16!=14!5!2! \dots

ProveErdős problem 373 - suranyiNumber theory0 α

Surányi was the first to conjecture that the only non-trivial solution to a!b!=n! is 6!7!=10! .

DisproveErdős problem 373 - suranyiNumber theory0 α

Surányi was the first to conjecture that the only non-trivial solution to a!b!=n! is 6!7!=10! .

ProveErdős problem 375Number theory0 α

Is Erdos375Prop true?

DisproveErdős problem 375Number theory0 α

Is Erdos375Prop true?

ProveErdős problem 376Number theory0 α

n

DisproveErdős problem 376Number theory0 α

n

ProveErdős problem 383Number theory0 α

k

DisproveErdős problem 383Number theory0 α

k

ProveErdős problem 385 - part iNumber theory0 α

F(n) := \max\{m + p(m) \mid \textrm{$m < n$ composite}\}\}

DisproveErdős problem 385 - part iNumber theory0 α

F(n) := \max\{m + p(m) \mid \textrm{$m < n$ composite}\}\}

ProveErdős problem 386 - twoNumber theory0 α

\binom{n}{2}

DisproveErdős problem 386 - twoNumber theory0 α

\binom{n}{2}

ProveErdős problem 39Number theory0 α

A\subset \mathbb{N}

DisproveErdős problem 39Number theory0 α

A\subset \mathbb{N}

ProveErdős problem 396Number theory0 α

k

DisproveErdős problem 396Number theory0 α

k

ProveErdős problem 398Number theory0 α

n = 4, 5, 7

DisproveErdős problem 398Number theory0 α

n = 4, 5, 7

ProveErdős problem 400 - part iNumber theory0 α

\sum_{n\leq x}g_k(n) \sim c_k x\log x

DisproveErdős problem 400 - part iNumber theory0 α

\sum_{n\leq x}g_k(n) \sim c_k x\log x

ProveErdős problem 406 - one twoNumber theory0 α

1

DisproveErdős problem 406 - one twoNumber theory0 α

1

ProveErdős problem 409 - sigma terminationNumber theory0 α

n > 1

DisproveErdős problem 409 - sigma terminationNumber theory0 α

n > 1

ProveErdős problem 41Number theory0 α

A \subset \mathbb{N}

DisproveErdős problem 41Number theory0 α

A \subset \mathbb{N}

ProveErdős problem 410Number theory0 α

σ_1(n) = σ(n)

DisproveErdős problem 410Number theory0 α

σ_1(n) = σ(n)

ProveErdős problem 412Number theory0 α

σ_1(n)=σ(n)

DisproveErdős problem 412Number theory0 α

σ_1(n)=σ(n)

ProveErdős problem 413 - part iNumber theory0 α

Are there infinitely many barriers for ω ?

DisproveErdős problem 413 - part iNumber theory0 α

Are there infinitely many barriers for ω ?

ProveErdős problem 414Number theory0 α

h_1(n) = h(n)

DisproveErdős problem 414Number theory0 α

h_1(n) = h(n)

ProveErdős problem 416 - part iNumber theory0 α

Let V(x) count the number of n\leqx such that ϕ(m)=n is solvable. Does V(2x)/V(x)\to2 ?

DisproveErdős problem 416 - part iNumber theory0 α

Let V(x) count the number of n\leqx such that ϕ(m)=n is solvable. Does V(2x)/V(x)\to2 ?

ProveErdős problem 428Number theory0 α

A\subseteq \mathbb{N}

DisproveErdős problem 428Number theory0 α

A\subseteq \mathbb{N}

ProveErdős problem 44Combinatorics0 α

**Erdős Problem 44:** Let N \geq 1 and A \subseteq {1,\dots,N} be a Sidon set. Is it true that, for any ε > 0, there exist M = M(ε) and\dots

DisproveErdős problem 44Combinatorics0 α

**Erdős Problem 44:** Let N \geq 1 and A \subseteq {1,\dots,N} be a Sidon set. Is it true that, for any ε > 0, there exist M = M(ε) and\dots

ProveErdős problem 445Number theory0 α

c>1/2

DisproveErdős problem 445Number theory0 α

c>1/2

ProveErdős problem 454Number theory0 α

Is it true that limsup (fun n => (f n - 2 * n.nth Prime : ℕ\infty)) atTop = ⊤ ?

DisproveErdős problem 454Number theory0 α

Is it true that limsup (fun n => (f n - 2 * n.nth Prime : ℕ\infty)) atTop = ⊤ ?

ProveErdős problem 455Number theory0 α

Let q : ℕ \to ℕ be a strictly increasing sequence of primes such that q (n + 2) - q (n + 1) \geq q (n + 1) - q n . Must\dots

DisproveErdős problem 455Number theory0 α

Let q : ℕ \to ℕ be a strictly increasing sequence of primes such that q (n + 2) - q (n + 1) \geq q (n + 1) - q n . Must\dots

ProveErdős problem 456 - part iiiNumber theory0 α

p

DisproveErdős problem 456 - part iiiNumber theory0 α

p

ProveErdős problem 458Number theory0 α

\operatorname{lcm}(1, \dots, n)

DisproveErdős problem 458Number theory0 α

\operatorname{lcm}(1, \dots, n)

ProveErdős problem 463Number theory0 α

f

DisproveErdős problem 463Number theory0 α

f

ProveErdős problem 479Number theory0 α

k\neq 1

DisproveErdős problem 479Number theory0 α

k\neq 1

ProveErdős problem 495Number theory0 α

\alpha,\beta \in \mathbb{R}

DisproveErdős problem 495Number theory0 α

\alpha,\beta \in \mathbb{R}

ProveErdős problem 50Number theory0 α

f

DisproveErdős problem 50Number theory0 α

f

ProveErdős problem 51Number theory0 α

A \subset \mathbb{N}

DisproveErdős problem 51Number theory0 α

A \subset \mathbb{N}

ProveErdős problem 517Complex functions0 α

If f(z) = \sum aₖzⁿₖ is an entire function (with aₖ \neq 0 for all k) such that nₖ / k \to \infty, is it true that f assumes every\dots

DisproveErdős problem 517Complex functions0 α

If f(z) = \sum aₖzⁿₖ is an entire function (with aₖ \neq 0 for all k) such that nₖ / k \to \infty, is it true that f assumes every\dots

ProveErdős problem 52Number theory0 α

A

DisproveErdős problem 52Number theory0 α

A

ProveErdős problem 535Combinatorics0 α

r \geq 3

DisproveErdős problem 535Combinatorics0 α

r \geq 3

ProveErdős problem 535 - first open caseCombinatorics0 α

r = 3

DisproveErdős problem 535 - first open caseCombinatorics0 α

r = 3

ProveErdős problem 564Combinatorics0 α

R_3(n)

DisproveErdős problem 564Combinatorics0 α

R_3(n)

ProveErdős problem 579Combinatorics0 α

\delta > 0

DisproveErdős problem 579Combinatorics0 α

\delta > 0

ProveErdős problem 600 - part iCombinatorics0 α

r \geq 2

DisproveErdős problem 600 - part iCombinatorics0 α

r \geq 2

ProveErdős problem 61Combinatorics0 α

c(H) > 0

DisproveErdős problem 61Combinatorics0 α

c(H) > 0

ProveErdős problem 617Combinatorics0 α

r\geq 3

DisproveErdős problem 617Combinatorics0 α

r\geq 3

ProveErdős problem 624Combinatorics0 α

X

DisproveErdős problem 624Combinatorics0 α

X

ProveErdős problem 647Number theory0 α

\tau(n)

DisproveErdős problem 647Number theory0 α

\tau(n)

ProveErdős problem 653Combinatorics0 α

x_1,\ldots,x_n\in \mathbb{R}^2

DisproveErdős problem 653Combinatorics0 α

x_1,\ldots,x_n\in \mathbb{R}^2

ProveErdős problem 66Number theory0 α

A \subset \mathbb{N}

DisproveErdős problem 66Number theory0 α

A \subset \mathbb{N}

ProveErdős problem 672Number theory0 α

n, n + d, ..., n + (k - 1)d

DisproveErdős problem 672Number theory0 α

n, n + d, ..., n + (k - 1)d

ProveErdős problem 677Number theory0 α

M(n, k)

DisproveErdős problem 677Number theory0 α

M(n, k)

ProveErdős problem 68Number theory0 α

\sum_{n=2}^\infty \frac{1}{n!-1}

DisproveErdős problem 68Number theory0 α

\sum_{n=2}^\infty \frac{1}{n!-1}

ProveErdős problem 680 - part iNumber theory0 α

n

DisproveErdős problem 680 - part iNumber theory0 α

n

ProveErdős problem 680 - part iiNumber theory0 α

k^2+1

DisproveErdős problem 680 - part iiNumber theory0 α

k^2+1

ProveErdős problem 681Number theory0 α

n

DisproveErdős problem 681Number theory0 α

n

ProveErdős problem 686 - fourNumber theory0 α

4

DisproveErdős problem 686 - fourNumber theory0 α

4

ProveErdős problem 686 - twenty fiveNumber theory0 α

25

DisproveErdős problem 686 - twenty fiveNumber theory0 α

25

ProveErdős problem 688 - part iiNumber theory0 α

\epsilon_n = o(1)

DisproveErdős problem 688 - part iiNumber theory0 α

\epsilon_n = o(1)

ProveErdős problem 695Number theory0 α

q_1 < q_2 < \cdots

DisproveErdős problem 695Number theory0 α

q_1 < q_2 < \cdots

ProveErdős problem 695 - upper BoundNumber theory0 α

q_1 < q_2 < \cdots

DisproveErdős problem 695 - upper BoundNumber theory0 α

q_1 < q_2 < \cdots

ProveErdős problem 699Number theory0 α

1 \le i < j \le n / 2

DisproveErdős problem 699Number theory0 α

1 \le i < j \le n / 2

ProveErdős problem 70 - omega times two fourLogic and foundations0 α

\mathfrak{c} \to (\omega \cdot 2, 4)^3_2

DisproveErdős problem 70 - omega times two fourLogic and foundations0 α

\mathfrak{c} \to (\omega \cdot 2, 4)^3_2

ProveErdős problem 701Combinatorics0 α

\mathcal{F}

DisproveErdős problem 701Combinatorics0 α

\mathcal{F}

ProveErdős problem 723 - eq 12Combinatorics0 α

It is open whether there exists a projective plane of order 12.

DisproveErdős problem 723 - eq 12Combinatorics0 α

It is open whether there exists a projective plane of order 12.

ProveErdős problem 749Number theory0 α

\epsilon>0

DisproveErdős problem 749Number theory0 α

\epsilon>0

ProveErdős problem 770 - part iNumber theory0 α

For every prime p, does the density of integers with h n = p exist?

DisproveErdős problem 770 - part iNumber theory0 α

For every prime p, does the density of integers with h n = p exist?

ProveErdős problem 770 - threeNumber theory0 α

It is probably true that h n = 3 for infinitely many n .

DisproveErdős problem 770 - threeNumber theory0 α

It is probably true that h n = 3 for infinitely many n .

ProveErdős problem 774Combinatorics0 α

Is every proportionately dissociated (infinite) set the union of a finite number of dissociated sets?

DisproveErdős problem 774Combinatorics0 α

Is every proportionately dissociated (infinite) set the union of a finite number of dissociated sets?

ProveErdős problem 779Number theory0 α

A Conjecture of Marian Deaconescu, see p.120 in https://doi.org/10.2307/2975810 [Needed to index shift in order to avoid trivial\dots

DisproveErdős problem 779Number theory0 α

A Conjecture of Marian Deaconescu, see p.120 in https://doi.org/10.2307/2975810 [Needed to index shift in order to avoid trivial\dots

ProveErdős problem 789 - sqCombinatorics0 α

h(n)

DisproveErdős problem 789 - sqCombinatorics0 α

h(n)

ProveErdős problem 812 - part iCombinatorics0 α

\frac{R(n+1)}{R(n)}\geq 1+c

DisproveErdős problem 812 - part iCombinatorics0 α

\frac{R(n+1)}{R(n)}\geq 1+c

ProveErdős problem 82Combinatorics0 α

F(n) / \log n \to \infty as n \to \infty

DisproveErdős problem 82Combinatorics0 α

F(n) / \log n \to \infty as n \to \infty

ProveErdős problem 821Number theory0 α

\epsilon>0

DisproveErdős problem 821Number theory0 α

\epsilon>0

ProveErdős problem 828Number theory0 α

a \in \mathbb{Z}

DisproveErdős problem 828Number theory0 α

a \in \mathbb{Z}

ProveErdős problem 828 - lehmer conjectureNumber theory0 α

n > 1

DisproveErdős problem 828 - lehmer conjectureNumber theory0 α

n > 1

ProveErdős problem 829Number theory0 α

A \subseteq \mathbb{N}

DisproveErdős problem 829Number theory0 α

A \subseteq \mathbb{N}

ProveErdős problem 835Combinatorics0 α

k>2

DisproveErdős problem 835Combinatorics0 α

k>2

ProveErdős problem 849Number theory0 α

t\geq1

DisproveErdős problem 849Number theory0 α

t\geq1

ProveErdős problem 85Combinatorics0 α

n

DisproveErdős problem 85Combinatorics0 α

n

ProveErdős problem 853 - part iNumber theory0 α

d_n = p_{n+1} - p_n

DisproveErdős problem 853 - part iNumber theory0 α

d_n = p_{n+1} - p_n

ProveErdős problem 853 - part iiNumber theory0 α

d_n = p_{n+1} - p_n

DisproveErdős problem 853 - part iiNumber theory0 α

d_n = p_{n+1} - p_n

ProveErdős problem 859Number theory0 α

c_1 / \log(t)^{c_2}

DisproveErdős problem 859Number theory0 α

c_1 / \log(t)^{c_2}

ProveErdős problem 873Number theory0 α

A = \{a_1 < a_2 < \dots\} \subseteq \mathbb{N}

DisproveErdős problem 873Number theory0 α

A = \{a_1 < a_2 < \dots\} \subseteq \mathbb{N}

ProveErdős problem 885Number theory0 α

k \geq 1

DisproveErdős problem 885Number theory0 α

k \geq 1

ProveErdős problem 886Number theory0 α

\epsilon>0

DisproveErdős problem 886Number theory0 α

\epsilon>0

ProveErdős problem 887 - part iiNumber theory0 α

K

DisproveErdős problem 887 - part iiNumber theory0 α

K

ProveErdős problem 889Number theory0 α

v(n,k)

DisproveErdős problem 889Number theory0 α

v(n,k)

ProveErdős problem 889 - generalNumber theory0 α

v_l(n) = \max_{k\geq l} v(n,k)

DisproveErdős problem 889 - generalNumber theory0 α

v_l(n) = \max_{k\geq l} v(n,k)

ProveErdős problem 89Convex and discrete geometry0 α

n

DisproveErdős problem 89Convex and discrete geometry0 α

n

ProveErdős problem 890 - part aNumber theory0 α

\omega_k(n)

DisproveErdős problem 890 - part aNumber theory0 α

\omega_k(n)

ProveErdős problem 890 - part bNumber theory0 α

\limsup_{n\to \infty}\left(\sum_{0\leq i < k}\omega(n+i)\right) \frac{\log\log n}{\log n}=1,

DisproveErdős problem 890 - part bNumber theory0 α

\limsup_{n\to \infty}\left(\sum_{0\leq i < k}\omega(n+i)\right) \frac{\log\log n}{\log n}=1,

ProveErdős problem 891Number theory0 α

2=p_1 < p_2 < \cdots

DisproveErdős problem 891Number theory0 α

2=p_1 < p_2 < \cdots

ProveErdős problem 893Combinatorics0 α

\lim_{n\to\infty} \frac{f(2n)}{f(n)}

DisproveErdős problem 893Combinatorics0 α

\lim_{n\to\infty} \frac{f(2n)}{f(n)}

ProveErdős problem 9Combinatorics0 α

Is the upper density of the set of odd numbers that cannot be expressed as a prime plus two powers of 2 positive?

DisproveErdős problem 9Combinatorics0 α

Is the upper density of the set of odd numbers that cannot be expressed as a prime plus two powers of 2 positive?

ProveErdős problem 91Convex and discrete geometry0 α

A\subset \mathbb{R}^2

DisproveErdős problem 91Convex and discrete geometry0 α

A\subset \mathbb{R}^2

ProveErdős problem 912Number theory0 α

c>0

DisproveErdős problem 912Number theory0 α

c>0

ProveErdős problem 912 - taoNumber theory0 α

c=\sqrt{2\pi}

DisproveErdős problem 912 - taoNumber theory0 α

c=\sqrt{2\pi}

ProveErdős problem 913 - infinite many 8 p sq sub one primesNumber theory0 α

p

DisproveErdős problem 913 - infinite many 8 p sq sub one primesNumber theory0 α

p

ProveErdős problem 930Number theory0 α

r

DisproveErdős problem 930Number theory0 α

r

ProveErdős problem 931Number theory0 α

k_1 \geq k_2 \geq 3

DisproveErdős problem 931Number theory0 α

k_1 \geq k_2 \geq 3

ProveErdős problem 932Number theory0 α

p_k

DisproveErdős problem 932Number theory0 α

p_k

ProveErdős problem 933Number theory0 α

n(n+1)=2^k3^lm

DisproveErdős problem 933Number theory0 α

n(n+1)=2^k3^lm

ProveErdős problem 936 - factorial add oneNumber theory0 α

n! + 1

DisproveErdős problem 936 - factorial add oneNumber theory0 α

n! + 1

ProveErdős problem 936 - factorial sub oneNumber theory0 α

n! - 1

DisproveErdős problem 936 - factorial sub oneNumber theory0 α

n! - 1

ProveErdős problem 936 - two pow add oneNumber theory0 α

2^n + 1

DisproveErdős problem 936 - two pow add oneNumber theory0 α

2^n + 1

ProveErdős problem 936 - two pow sub oneNumber theory0 α

2^n - 1

DisproveErdős problem 936 - two pow sub oneNumber theory0 α

2^n - 1

ProveErdős problem 942Number theory0 α

c > 0

DisproveErdős problem 942Number theory0 α

c > 0

ProveErdős problem 943Number theory0 α

A

DisproveErdős problem 943Number theory0 α

A

ProveErdős problem 944Number theory0 α

k \ge 4

DisproveErdős problem 944Number theory0 α

k \ge 4

ProveErdős problem 945Number theory0 α

F(x) \leq (\log x)^{O(1)}

DisproveErdős problem 945Number theory0 α

F(x) \leq (\log x)^{O(1)}

ProveErdős problem 949Combinatorics0 α

S \subseteq \mathbb{R}

DisproveErdős problem 949Combinatorics0 α

S \subseteq \mathbb{R}

ProveErdős problem 950 - part iNumber theory0 α

\liminf f(n)=1

DisproveErdős problem 950 - part iNumber theory0 α

\liminf f(n)=1

ProveErdős problem 950 - part iiNumber theory0 α

\limsup f(n)=\infty

DisproveErdős problem 950 - part iiNumber theory0 α

\limsup f(n)=\infty

ProveErdős problem 950 - part iiiNumber theory0 α

f(n)=o(\log\log n)

DisproveErdős problem 950 - part iiiNumber theory0 α

f(n)=o(\log\log n)

ProveErdős problem 951Number theory0 α

If 1 < a 0 < ... has property Erdos951Prop, is it true that #{a i \leq x} \leq π x ?

DisproveErdős problem 951Number theory0 α

If 1 < a 0 < ... has property Erdos951Prop, is it true that #{a i \leq x} \leq π x ?

ProveErdős problem 952Number theory0 α

x_1,x_2,\ldots

DisproveErdős problem 952Number theory0 α

x_1,x_2,\ldots

ProveErdős problem 962Number theory0 α

\log k(n) \le (\log n)^{(1/2 + o(1))}

DisproveErdős problem 962Number theory0 α

\log k(n) \le (\log n)^{(1/2 + o(1))}

ProveErdős problem 972Number theory0 α

\alpha > 1

DisproveErdős problem 972Number theory0 α

\alpha > 1

ProveErdős problem 975Number theory0 α

f \in \mathbb{Z}[x]

DisproveErdős problem 975Number theory0 α

f \in \mathbb{Z}[x]

ProveErdős problem 978 - part iiNumber theory0 α

k>3

DisproveErdős problem 978 - part iiNumber theory0 α

k>3

ProveErdős problem 978 - part iiiNumber theory0 α

Does n ^ 4 + 2 represent infinitely many squarefree numbers?

DisproveErdős problem 978 - part iiiNumber theory0 α

Does n ^ 4 + 2 represent infinitely many squarefree numbers?

ProveErdős problem 979Number theory0 α

k ≥ 2

DisproveErdős problem 979Number theory0 α

k ≥ 2

ProveErdős problem 98Convex and discrete geometry0 α

h(n)

DisproveErdős problem 98Convex and discrete geometry0 α

h(n)

ProveErdős problem 982Convex and discrete geometry0 α

n

DisproveErdős problem 982Convex and discrete geometry0 α

n

ProveErdős problem 985Number theory0 α

p

DisproveErdős problem 985Number theory0 α

p

ProveErdős problem 99Convex and discrete geometry0 α

1

DisproveErdős problem 99Convex and discrete geometry0 α

1

ProveFermat - infinite fermat primesNumber theory0 α

Are there infinitely many Fermat primes?

DisproveFermat - infinite fermat primesNumber theory0 α

Are there infinitely many Fermat primes?

ProveGauss Circle Problem - error is Big ONumber theory0 α

|E(r)| = O\left(r^{1/2 + o(1)}\right)

DisproveGauss Circle Problem - error is Big ONumber theory0 α

|E(r)| = O\left(r^{1/2 + o(1)}\right)

ProveGoldbach ConjectureNumber theory0 α

Can every even integer greater than 2 be written as the sum of two primes?

DisproveGoldbach ConjectureNumber theory0 α

Can every even integer greater than 2 be written as the sum of two primes?

ProveGoormaghtighNumber theory0 α

31

DisproveGoormaghtighNumber theory0 α

31

ProveGreen's open problem 12Combinatorics0 α

G

DisproveGreen's open problem 12Combinatorics0 α

G

ProveGreen's open problem 15Combinatorics0 α

f : \mathbb{N} \to \mathbb{Z}

DisproveGreen's open problem 15Combinatorics0 α

f : \mathbb{N} \to \mathbb{Z}

ProveGreen's open problem 18Combinatorics0 α

G

DisproveGreen's open problem 18Combinatorics0 α

G

ProveGreen's open problem 2Number theory0 α

A \subset \mathbf{Z}

DisproveGreen's open problem 2Number theory0 α

A \subset \mathbf{Z}

ProveGreen's open problem 24 - conjectureCombinatorics0 α

\left(\frac{1}{3} + o(1)\right) n^2

DisproveGreen's open problem 24 - conjectureCombinatorics0 α

\left(\frac{1}{3} + o(1)\right) n^2

ProveGreen's open problem 32Combinatorics0 α

p

DisproveGreen's open problem 32Combinatorics0 α

p

ProveGreen's open problem 33Combinatorics0 α

q

DisproveGreen's open problem 33Combinatorics0 α

q

ProveGreen's open problem 36 - cks 05Combinatorics0 α

Variant using the exact simultaneous double product property from [CKS05, 4.1].

DisproveGreen's open problem 36 - cks 05Combinatorics0 α

Variant using the exact simultaneous double product property from [CKS05, 4.1].

ProveGreen's open problem 39Combinatorics0 α

A \subset \mathbb{Z}/p\mathbb{Z}

DisproveGreen's open problem 39Combinatorics0 α

A \subset \mathbb{Z}/p\mathbb{Z}

ProveGreen's open problem 40Combinatorics0 α

f(r) \to \infty

DisproveGreen's open problem 40Combinatorics0 α

f(r) \to \infty

ProveGreen's open problem 40 - f two eq oneCombinatorics0 α

It is not known whether f(2) = 1 [Gr24]

DisproveGreen's open problem 40 - f two eq oneCombinatorics0 α

It is not known whether f(2) = 1 [Gr24]

ProveGreen's open problem 40 - arbitrary subsetsCombinatorics0 α

\tilde{f}(r) \to \infty

DisproveGreen's open problem 40 - arbitrary subsetsCombinatorics0 α

\tilde{f}(r) \to \infty

ProveGreen's open problem 41 - polynomial boundGeometry0 α

\varepsilon^{-C}

DisproveGreen's open problem 41 - polynomial boundGeometry0 α

\varepsilon^{-C}

ProveGreen's open problem 50Combinatorics0 α

A \subset \mathbb{F}_2^n

DisproveGreen's open problem 50Combinatorics0 α

A \subset \mathbb{F}_2^n

ProveGreen's open problem 58Combinatorics0 α

A, B ⊆ \{1, \dots, N\}

DisproveGreen's open problem 58Combinatorics0 α

A, B ⊆ \{1, \dots, N\}

ProveGreen's open problem 60Number theory0 α

c > 0

DisproveGreen's open problem 60Number theory0 α

c > 0

ProveGreen's open problem 62Number theory0 α

p

DisproveGreen's open problem 62Number theory0 α

p

ProveGreen's open problem 66Number theory0 α

X - \frac{1}{10}X^{1/4}

DisproveGreen's open problem 66Number theory0 α

X - \frac{1}{10}X^{1/4}

ProveGreen's open problem 7 - positive densityNumber theory0 α

Does Ulam's sequence have positive density?

DisproveGreen's open problem 7 - positive densityNumber theory0 α

Does Ulam's sequence have positive density?

ProveGreen's open problem 72Combinatorics0 α

N

DisproveGreen's open problem 72Combinatorics0 α

N

ProveGreen's open problem 9 - iiCombinatorics0 α

r_5(N) \ll N(\log N)^{-c}

DisproveGreen's open problem 9 - iiCombinatorics0 α

r_5(N) \ll N(\log N)^{-c}

ProveGreen's open problem 9 - iiiCombinatorics0 α

r_4(\mathbf{F}_5^n) \ll N^{1-c}

DisproveGreen's open problem 9 - iiiCombinatorics0 α

r_4(\mathbf{F}_5^n) \ll N^{1-c}

ProveHadamardLinear algebra0 α

n = 4k

DisproveHadamardLinear algebra0 α

n = 4k

ProveHardy Littlewood - first hardy littlewood conjectureNumber theory0 α

P = (m_1, \dots, m_k)

DisproveHardy Littlewood - first hardy littlewood conjectureNumber theory0 α

P = (m_1, \dots, m_k)

ProveHardy Littlewood - second hardy littlewood conjectureNumber theory0 α

x, y \geq 2

DisproveHardy Littlewood - second hardy littlewood conjectureNumber theory0 α

x, y \geq 2

ProveIdoneal Completeness - idoneal numbers completenessNumber theory0 α

Idoneal numbers completeness conjecture.

DisproveIdoneal Completeness - idoneal numbers completenessNumber theory0 α

Idoneal numbers completeness conjecture.

ProveInscribed SquareGeometry0 α

**Inscribed square problem** Does every Jordan curve admit an inscribed square?

DisproveInscribed SquareGeometry0 α

**Inscribed square problem** Does every Jordan curve admit an inscribed square?

ProveInverse GaloisField theory and polynomials0 α

The **Inverse Galois Problem**: every finite group is isomorphic to the Galois group of a Galois extension of the rationals.

DisproveInverse GaloisField theory and polynomials0 α

The **Inverse Galois Problem**: every finite group is isomorphic to the Galois group of a Galois extension of the rationals.

ProveIrrational - euler Mascheroni ConstantSpecial functions0 α

\gamma

DisproveIrrational - euler Mascheroni ConstantSpecial functions0 α

\gamma

ProveKummer VandiverNumber theory0 α

p

DisproveKummer VandiverNumber theory0 α

p

ProveLegendre ConjectureNumber theory0 α

Does there always exist at least one prime between consecutive perfect squares?

DisproveLegendre ConjectureNumber theory0 α

Does there always exist at least one prime between consecutive perfect squares?

ProveLehmer Mahler Measure ProblemNumber theory0 α

Let M(f) denote the Mahler measure of f . There exists a constant μ>1 such that for any f(x)\inℤ[x], M(f)>1 \to M(f)\geqμ .

DisproveLehmer Mahler Measure ProblemNumber theory0 α

Let M(f) denote the Mahler measure of f . There exists a constant μ>1 such that for any f(x)\inℤ[x], M(f)>1 \to M(f)\geqμ .

ProveLehmer TotientNumber theory0 α

n > 1

DisproveLehmer TotientNumber theory0 α

n > 1

ProveLemoineNumber theory0 α

n ≥ 7

DisproveLemoineNumber theory0 α

n ≥ 7

ProveMersenne - catalans mersenne conjectureNumber theory0 α

c_0, \ldots, c_4

DisproveMersenne - catalans mersenne conjectureNumber theory0 α

c_0, \ldots, c_4

ProveMersenne - infinitely many mersenne primesNumber theory0 α

Are there infinitely many Mersenne primes?

DisproveMersenne - infinitely many mersenne primesNumber theory0 α

Are there infinitely many Mersenne primes?

ProveNormality Of Pi - pi normal base tenNumber theory0 α

\pi

DisproveNormality Of Pi - pi normal base tenNumber theory0 α

\pi

ProveOppermannNumber theory0 α

x \ge 2

DisproveOppermannNumber theory0 α

x \ge 2

ProvePerfect Numbers - odd perfect number conjectureNumber theory0 α

**Odd Perfect Number Conjecture.** The Odd Perfect Number Conjecture states that all perfect numbers are\dots

DisprovePerfect Numbers - odd perfect number conjectureNumber theory0 α

**Odd Perfect Number Conjecture.** The Odd Perfect Number Conjecture states that all perfect numbers are\dots

ProvePollocks Conjecture - pollock tetrahedralNumber theory0 α

5

DisprovePollocks Conjecture - pollock tetrahedralNumber theory0 α

5

ProvePrimes And Perfect Squares - infinite prime sq add oneNumber theory0 α

p

DisprovePrimes And Perfect Squares - infinite prime sq add oneNumber theory0 α

p

ProveRegular Primes - regularprime conjectureNumber theory0 α

Conjecture: The set of regular primes is infinite.

DisproveRegular Primes - regularprime conjectureNumber theory0 α

Conjecture: The set of regular primes is infinite.

ProveRiemann HypothesisNumber theory0 α

\frac{1}{2}

DisproveRiemann HypothesisNumber theory0 α

\frac{1}{2}

ProveTwin PrimesNumber theory0 α

Are there infinitely many primes p such that p + 2 is prime?

DisproveTwin PrimesNumber theory0 α

Are there infinitely many primes p such that p + 2 is prime?

ProveErdős problem 196CombinatoricsSolved-

\mathbb{N}

DisproveErdős problem 196CombinatoricsSolved-

\mathbb{N}

ProveErdős problem 272 - szabo strongCombinatoricsSolved-

t

DisproveErdős problem 272 - szabo strongCombinatoricsSolved-

t

ProveErdős problem 726Number theorySolved-

n\to \infty

DisproveErdős problem 726Number theorySolved-

n\to \infty

ProveErdős problem 96Convex and discrete geometrySolved-

n

DisproveErdős problem 96Convex and discrete geometrySolved-

n

ProveGreen's open problem 47Number theorySolved-

Suppose that a large sieve process leaves a set of quadratic size. Is that set quadratic? The following very particular instance\dots

DisproveGreen's open problem 47Number theorySolved-

Suppose that a large sieve process leaves a set of quadratic size. Is that set quadratic? The following very particular instance\dots

ProveGreen's open problem 51 - one halfCombinatoricsSolved-

A \subset \mathbb{F}_2^n

DisproveGreen's open problem 51 - one halfCombinatoricsSolved-

A \subset \mathbb{F}_2^n