clopen.solutions

Open problems

980 registered problems.

OP-00918 Open
The Hardy–Littlewood prime k-tuples conjecture
NT · Hardy–Littlewood conjectures · prime constellations · prime k-tuples · singular series
OP-00919 Open
The Hardy–Littlewood asymptotic formula for Goldbach representations
NT · additive prime number theory · Goldbach's conjecture · Hardy–Littlewood conjectures · singular series
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-00921 Open
Representations n = ap + bp′ by two primes with fixed coefficients
NT · additive prime number theory · Goldbach's conjecture · Hardy–Littlewood conjectures · singular series
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-00925 Open
Representations n = am² + bm + p by a quadratic and a prime
NT · additive prime number theory · Hardy–Littlewood conjectures · quadratic polynomials
OP-00926 Open
Every large non-square is a prime plus a square
NT · additive prime number theory · Hardy–Littlewood conjectures · sums of a prime and a square
OP-00927 Open
Every large odd number is a prime plus twice a square
NT · additive prime number theory · Goldbach's other conjecture · Hardy–Littlewood conjectures
OP-00928 Open
Primes of the form m³ + k
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials
OP-00929 Open
Every large non-cube is a prime plus a cube
NT · additive prime number theory · cubic residues · Hardy–Littlewood conjectures
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