Dan Brumleve
Reputation
10,990
88/100 score
 Mar 28 comment Complement of SEMIPRIME is in NP If you ignore that trick and include the entire prime factorization, you can still take $c = 1 + \epsilon$: an $a$-digit number times a $b$-digit number is an $(a+b)$-digit number. Mar 19 comment Mathematicians shocked(?) to find pattern in prime numbers The Quanta article states that the consecutive prime bias is a prediction of the k-tuples conjecture. It seems straightforward to estimate the counts using it: take the sum of the k-tuples formula (modified slightly) over all the constellations consisting of two primes whose gap is in whichever congruence class mod $p$. And we could do the same thing to estimate the long-range repulsion, we just have to include a lot of additional constellations. If those calculations are consistent with the data then I guess the phenomena can be seen as evidence for the k-tuples conjecture. Mar 18 comment Can a complex number be prime? I found a great story with appearances by Liouville and Cauchy. Thanks Daniel. Mar 18 comment Can a complex number be prime? I'm curious to see the fake FLT proof. Mar 18 comment If more than one prime number satisfies a given congruence, must an infinite number of primes satisfy that congruence? Maybe you are looking for Dirichlet's theorem? Mar 17 comment Mathematicians shocked(?) to find pattern in prime numbers That's really amazing. I verified it for $p=7$ and tried it for some other small values of $p$ and they all repel. I also tried excluding the primes immediately before and after $q$ to make sure that consecutive primes aren't causing the entire effect, and the repulsion is still present. Is there a reference for this or did you discover it yourself? Why does this happen? I'm reminded of quasirandomness. Mar 16 revised Does the colon in function notation stand for “such that”? added 12 characters in body Mar 16 answered Does the colon in function notation stand for “such that”? Mar 16 answered Twin Prime Related Material Mar 15 comment Are there any instances of significant progress deriving from mathematical 'silliness'? Not downvoter but I think it would help to narrow the question. Lots of mathematics has its origins in doing things deliberately incorrectly, like subtracting a larger number from a smaller one, or taking the square root of a negative number. Mar 15 comment Are there any instances of significant progress deriving from mathematical 'silliness'? Conway's look-and-say sequence comes to mind but I'm not sure if it is silly in the same sense that you mean. Mar 15 answered Difficulty in giving input of integral to Wolframalpha Mar 15 revised Difficulty in giving input of integral to Wolframalpha added 9 characters in body Mar 15 revised Can anybody help me with math expressions? edited tags Mar 15 comment Can anybody help me with math expressions? Are you sure you are allowed to use each number more than once? That makes it easy and also tedious, a poor homework problem. Mar 15 comment Can anybody help me with math expressions? For this type of problem you are usually allowed to concatenate, and also use powers. That will help you get some of the larger ones. For example, $4^3+2+1=67$, $42+31=73$. Mar 15 comment Mathematicians shocked(?) to find pattern in prime numbers Here is a 2010 paper considering the same question mod $4$. I found it linked by a commenter in the Quanta article. Mar 15 comment Mathematicians shocked(?) to find pattern in prime numbers I caught that sentence too and also wondered if it had actually been proved, and if so what the big deal is. Reminds me of the situation with Chebyshev's bias. Your argument for why the disparity exists for small primes makes sense to me, but I am curious how it shakes out quantitatively. I also read this article with an even catchier title. Excellent question and cheers. Mar 13 comment Is there an expression for a function that maps integers to one and non-integers to zero? Is allowing limits the same as allowing derivatives? Mar 13 comment Is there an expression for a function that maps integers to one and non-integers to zero? Unfortunately no, that function is identically $0$ (regardless of how one defines $0^0$), for example: wolframalpha.com/input/…