clopen.solutions

Open problems

980 registered problems.

OP-00004 Open
Primes of the form n² + 1
NT · Landau's problems · primes represented by polynomials
OP-00020 Solution claimed
The Gaussian moat problem
NT · Erdős problems · Gaussian primes
OP-00920 Open
The Hardy–Littlewood asymptotic formula for prime pairs with a given difference
NT · Hardy–Littlewood conjectures · prime gaps · singular series · twin primes
OP-00922 Open
Prime solutions of the linear equation ap′ − bp = k
NT · Hardy–Littlewood conjectures · linear equations in primes · prime pairs · singular series
OP-00923 Open
The Hardy–Littlewood asymptotic formula for primes of the form m² + 1
NT · Hardy–Littlewood conjectures · Landau's problems · primes represented by polynomials
OP-00924 Open
Primes represented by a quadratic polynomial am² + bm + c
NT · Bunyakovsky conjecture · Hardy–Littlewood conjectures · primes represented by polynomials
OP-00928 Open
Primes of the form m³ + k
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials
OP-00930 Open
Primes of the form l³ + m³ + k
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials · sums of cubes
OP-00931 Open
Asymptotic count of primes that are sums of three positive cubes
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials · sums of cubes
OP-00932 Open
Prime pairs m² + 1, m² + 3
NT · Hardy–Littlewood conjectures · prime pairs · primes represented by polynomials
OP-00944 Open
A composite number in a sumset below the square-root threshold
NT · inverse Goldbach problem · large sieve · primes · sumsets
OP-00948 Open
Primes p for which p − 2 has an odd number of prime factors
NT · Liouville function · parity problem · shifted primes · twin primes