Problems · OpenFrontiers

OP-9933Mathematics · generalStatus unassessed

Equational Theories

Formal Conjectures· Specialist source · status unassessed

OP-9932CombinatoricsStatus unassessed

Beaver Math Olympiad (BMO)

Formal Conjectures· Specialist source · status unassessed

OP-9931CombinatoricsStatus unassessed

Tao's Optimization constant 1a / An autocorrelation constant related to Sidon sets

Formal Conjectures· Specialist source · status unassessed

OP-9930CombinatoricsStatus unassessed

Open Quantum Problem 35: existence of absolutely maximally entangled pure states

Formal Conjectures· Specialist source · status unassessed

OP-9929AlgebraStatus unassessed

Open Quantum Problem 23: SIC-POVMs

Formal Conjectures· Specialist source · status unassessed

OP-9928CombinatoricsStatus unassessed

Open Quantum Problem 13: Mutually unbiased bases

Formal Conjectures· Specialist source · status unassessed

OP-9927Number theoryStatus unassessed

Recurrence $a(n) = (a(n-1) + a(n-2)) \pmod n$

Recurrence a(n) = (a(n-1) + a(n-2)) pmod n

Formal Conjectures· Specialist source · status unassessed

OP-9926Number theoryStatus unassessed

Euclid-Mullin sequence

Formal Conjectures· Specialist source · status unassessed

OP-9925Number theoryStatus unassessed

$\gcd(\mathrm{numerator}(H_n), n!)$

gcd( mathrm numerator (H n), n!)

Formal Conjectures· Specialist source · status unassessed

OP-9924Number theoryStatus unassessed

Product of composite numbers in triangular intervals

Formal Conjectures· Specialist source · status unassessed

OP-9923Number theoryStatus unassessed

Tug of war score between prime gap increases and decreases

Formal Conjectures· Specialist source · status unassessed

OP-9922Number theoryStatus unassessed

Number of pairs of twin primes between $n^2$ and $(n+1)^2$

Number of pairs of twin primes between n^2 and (n+1)^2

Formal Conjectures· Specialist source · status unassessed

OP-9921Number theoryStatus unassessed

Smallest prime formed by concatenation $n, n-1, \dots, n-k$

Smallest prime formed by concatenation n, n-1, dots, n-k

Formal Conjectures· Specialist source · status unassessed

OP-9920Number theoryStatus unassessed

Expansion of $(1 - x)/(1 - 2 x + 3 x^2)$

Expansion of (1 - x)/(1 - 2 x + 3 x^2)

Formal Conjectures· Specialist source · status unassessed

OP-9919Number theoryStatus unassessed

Binary representation of primes that divide a number, in decimal

Formal Conjectures· Specialist source · status unassessed

OP-9918Number theoryStatus unassessed

Smallest $r$ such that (concatenation of $n$ , $r$ times) $\cdot 10 + 1$ is prime

Smallest r such that (concatenation of n , r times) cdot 10 + 1 is prime

Formal Conjectures· Specialist source · status unassessed

OP-9917Number theoryStatus unassessed

Smallest prime $p$ such that $p + n$ is an $n$ -th power

Smallest prime p such that p + n is an n -th power

Formal Conjectures· Specialist source · status unassessed

OP-9916Number theoryStatus unassessed

Smallest palindrome with exactly $n$ divisors

Smallest palindrome with exactly n divisors

Formal Conjectures· Specialist source · status unassessed

OP-9915Number theoryStatus unassessed

Primes of the form 2^n + 2^i + 1

Formal Conjectures· Specialist source · status unassessed

OP-9914Number theoryStatus unassessed

Denominator of $\sum_{k=1}^n k^{\mu(k)}$

Denominator of sum k=1 ^n k^ mu(k)

Formal Conjectures· Specialist source · status unassessed

OP-9913Number theoryStatus unassessed

Number of prime powers strictly between $n$ -th prime and $(n+1)$ -th prime

Number of prime powers strictly between n -th prime and (n+1) -th prime

Formal Conjectures· Specialist source · status unassessed

OP-9912Number theoryStatus unassessed

$a(n) = \sum_{k=0}^n \binom{2k}{k}^3$

a(n) = sum k=0 ^n binom 2k k ^3

Formal Conjectures· Specialist source · status unassessed

OP-9911Number theoryStatus unassessed

Least prime $\ge n$

Least prime ge n

Formal Conjectures· Specialist source · status unassessed

OP-9910Number theoryStatus unassessed

Least $k > 0$ such that $(k+1)(k+2)\cdots(k+n) + 1$ is prime

Least k 0 such that (k+1)(k+2) cdots(k+n) + 1 is prime

Formal Conjectures· Specialist source · status unassessed

OP-9909Number theoryStatus unassessed

Smallest $m > 0$ such that $n \cdot 2^m + 1$ is prime

Smallest m 0 such that n cdot 2^m + 1 is prime

Formal Conjectures· Specialist source · status unassessed

Equational Theories

Beaver Math Olympiad (BMO)

Tao's Optimization constant 1a / An autocorrelation constant related to Sidon sets

Open Quantum Problem 35: existence of absolutely maximally entangled pure states

Open Quantum Problem 23: SIC-POVMs

Open Quantum Problem 13: Mutually unbiased bases

Recurrence a(n)=(a(n−1)+a(n−2))(modn)a(n) = (a(n-1) + a(n-2)) \pmod na(n)=(a(n−1)+a(n−2))(modn)

Euclid-Mullin sequence

gcd⁡(numerator(Hn),n!)\gcd(\mathrm{numerator}(H_n), n!)gcd(numerator(Hn​),n!)

Product of composite numbers in triangular intervals

Tug of war score between prime gap increases and decreases

Number of pairs of twin primes between n2n^2n2 and (n+1)2(n+1)^2(n+1)2

Smallest prime formed by concatenation n,n−1,…,n−kn, n-1, \dots, n-kn,n−1,…,n−k

Expansion of (1−x)/(1−2x+3x2)(1 - x)/(1 - 2 x + 3 x^2)(1−x)/(1−2x+3x2)

Binary representation of primes that divide a number, in decimal

Smallest rrr such that (concatenation of nnn, rrr times) ⋅10+1\cdot 10 + 1⋅10+1 is prime

Smallest prime ppp such that p+np + np+n is an nnn-th power

Smallest palindrome with exactly nnn divisors

Primes of the form 2^n + 2^i + 1

Denominator of ∑k=1nkμ(k)\sum_{k=1}^n k^{\mu(k)}∑k=1n​kμ(k)

Number of prime powers strictly between nnn-th prime and (n+1)(n+1)(n+1)-th prime

a(n)=∑k=0n(2kk)3a(n) = \sum_{k=0}^n \binom{2k}{k}^3a(n)=∑k=0n​(k2k​)3

Least prime ≥n\ge n≥n

Least k>0k > 0k>0 such that (k+1)(k+2)⋯(k+n)+1(k+1)(k+2)\cdots(k+n) + 1(k+1)(k+2)⋯(k+n)+1 is prime

Smallest m>0m > 0m>0 such that n⋅2m+1n \cdot 2^m + 1n⋅2m+1 is prime

Recurrence $a(n) = (a(n-1) + a(n-2)) \pmod n$

$\gcd(\mathrm{numerator}(H_n), n!)$

Number of pairs of twin primes between $n^2$ and $(n+1)^2$

Smallest prime formed by concatenation $n, n-1, \dots, n-k$

Expansion of $(1 - x)/(1 - 2 x + 3 x^2)$

Smallest $r$ such that (concatenation of $n$ , $r$ times) $\cdot 10 + 1$ is prime

Smallest prime $p$ such that $p + n$ is an $n$ -th power

Smallest palindrome with exactly $n$ divisors

Denominator of $\sum_{k=1}^n k^{\mu(k)}$

Number of prime powers strictly between $n$ -th prime and $(n+1)$ -th prime

$a(n) = \sum_{k=0}^n \binom{2k}{k}^3$

Least prime $\ge n$

Least $k > 0$ such that $(k+1)(k+2)\cdots(k+n) + 1$ is prime

Smallest $m > 0$ such that $n \cdot 2^m + 1$ is prime