(graph theory) A conjecture concerning the connection between graph coloring and the tensor product of graphs. A counterexample was found in 2019.

(number theory) The conjecture that, for any positive even number n, there are infinitely many prime gaps of size n.

(number theory) The conjecture that, for a finite set of linear forms a₁ + b₁n, a₂ + b₂n, ..., aₖ + bₖn with bᵢ ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this.

(number theory) A conjecture relating to the conductor and the discriminant of an elliptic curve, equivalent in a slightly modified form to the abc conjecture.

(number theory) The conjecture that there are at least four prime numbers between (pₙ)² and (pₙ₊₁)², where pₙ is the nth prime number, for every n ≥ 2.

(mathematics) The conjecture that every domain of ℝᵈ (i.e. subset of ℝᵈ with positive finite Lebesgue measure) is a spectral set if and only if it tiles ℝᵈ by translation.

(mathematics) A conjecture in combinatorial number theory, stating that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times).

(number theory) An estimate for the size of gaps between consecutive prime numbers, stating that p_n+1-p_n=O(( log p_n)²), where pₙ denotes the nth prime number, O is big O notation, and log is the natural logarithm.

(mathematics) A conjecture concerning the relationship between the locations of roots and critical points of a polynomial function of a complex variable. It states that for a polynomial f(z)=(z-r_1)⋯(z-r_n), qquad (n>2) with all roots r₁, ..., rₙ inside the closed unit disk |z| ≤ 1, each of the n roots is at a distance no more than 1 from at least one critical point.

(mathematics) Synonym of Sendov's conjecture