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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/…