If a solution of the unsolved conjectures already exists, please leave a comment.

**Conj. 1: (Solved)**

For any non-negative real number , there exists a set, of which strict Hausdorff Dimension is equal to .

Fields: Measure Theory, Real Analysis

Proposed: 02.24.15

Solved: 03.16.15

The general outline is presented in the post, CONSTRUCTING A SET WITH ARBITRARY STRICT HAUSDORFF DIMENSION

**Conj. 2: (Unsolved)**

Let be a prime. Let denote the smallest primitive root of . Then, is bounded, while diverges.

Fields: Elementary Number Theory

Proposed: 10.28.14

**Conj. 3: (Solved)**

Let be a set of primes. The supremum of such that diverges is .

Fields: Analytic Number Theory

Proposed: 02.26.16

Solved: 03.17.16

The general outline is presented in the post, The Half-Plane of Convergence of Zeta Function, and it begot a new conjecture, **Conj. 4**.

**Conj. 4: (Unsolved)**

Let us define Prime Zeta Function as where is a set of primes. The domain of is all complex plane except like Riemann Zeta Function.

Fields: Analytic Number Theory

Proposed: 03.17.16

The post is still in progress.