Are there infinitely many semi primes of the form x2+2xx^2 + 2x for integral xx?

My professor showed the class 1000 dollars and said he’d give it to whoever could prove it… Obviously he’s not serious but in having a tough time wrestling with this problem. Answer It is likely that no one in the class will collect. Since x2+2x=x(x+2), for x>2 we have x2+2x is semiprime if and only … Read more

Invariant Subspace Problem

Louis de Branges had a paper on his homepage claiming a solution for the Invariant Subspace Problem. But I don’t see that paper anymore, though he still has a “proof” of Riemann Hypothesis on his website. Does anyone know whether he actually admitted his proof of the Invariant Subspace Problem was wrong? Or someone pointed … Read more

An open problem on general topology

There is an open problem in this paper: J. van Mill, V.V. Tkachuk, R.G. Wilson, “Classes defined by stars and neighbourhood assignments“, Topology and its Applications, Vol. 154, Issue 10, 2007, pp. 2127–2134. Problem 4.8. Is a regular star compact space metrizable if it has a Gδ-diagonal? A topological space X is said to be … Read more

Open problems in Banach spaces? universal spaces

I have gathered a list of universality problems in Banach spaces which have been solved: The non existence of a separable reflexive space universal for the class of separable reflexive spaces. If a space is universal for the class of separable reflexive spaces, then it is universal for the class of separable Banach spaces. There … Read more

Up to which value is Rassias’ conjecture verified?

I came across this conjecture: Rassias’ conjecture Up to which p has this conjecture be verified ? Are there intermediate results related to this conjecture ? The conjecture can be formulated in this way : For every prime p>2, there is a prime q, such that (p−1)q−1 is prime. The following PARI/GP-program shows, that for … Read more

General mathematical consensus on the correct answer to each Millenium Prize Problem

This question is an extension of Open mathematical questions for which we really, really have no idea what the answer is, although it may immediately get closed as vague and primarily opinion-based. For each Millenium Prize Problem, how confident is the general mathematical community of the actual correct answer? For example, it’s my understanding that … Read more

Theorems in the distribution of the primes without elementary proofs

From the turn of the 20th century, the thought of an elementary proof of the prime number theorem was the obvious holy grail for elementary methods, but after the work of Selberg and Erdos in the 40s failed to open up the new avenues that some had hoped, it seems that finding elementary proofs for … Read more

Balanced weight perfect matching

Given an undirected graph G=(V,E), edge weight we ∀e∈E, I’m interested in the following problem. Find a perfect matching M⊆E that minimizes (max. Does this problem generalize/reduce to an existing problem? I can find max weight perfect matching, but not exactly a “balanced weight perfect matching”. Any thoughts would be helpful. Answer AttributionSource : Link , … Read more

Open problems in Proof theory and Logic

There are numerous questions in the same form: “What are some open problems in mathematical logic”. So for this we know: Shelahs “Logical Dreams” Logical Dreams Friedmans “102 Problems in mathematical logic” Friedman’s list my first question is: Is there somewhere an updated list of these problems (which of them are solved)? and now a … Read more