Aug 25, 2022 · The goal of this question is to find if other methods exist to generate arbitrarily long sequences of consecutive numbers without primes. I started searching for other formulas and …

When I took basic number-theory course there was this exercise to find 2000 consecutive numbers. And of course it's well known that the trick to take numbers of the form $$ (n+1)!+m, \\quad 2 \\leq ...

Basically, on average, how many times one should roll to expect two consecutive sixes?

I need help proving that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite. The hint that came with the ...

Jun 17, 2015 · But the sum of a number of consecutive odd numbers is the square of that number. Therefore, the sum of $n$ consecutive $k^3$ starting with $1$ is $ [n (n+1)/2]^2$.

Proof: Sequence of n consecutive natural numbers containing no primes (Velleman P158 Thm 3.7.3) Ask Question Asked 12 years, 2 months ago Modified 11 years, 10 months ago

How can we prove that the product of $n$ consecutive integers is divisible by $n$ factorial? Note: In this subsequent question and the comments here the OP has clarified that he seeks a proof that "does …

Aug 6, 2018 · Additionally, Is it possible to have $1000$ consecutive natural numbers with exactly $12$ primes between them? I have an intuition that we have to form a recurrsive relation and solve it.

Aug 11, 2021 · Earlier today I saw a question about binary sequences of length $n$ that contain no $3$ consecutive $1$ s or $0$ s. I want to generalize the problem a little and count the number of …

Jun 6, 2017 · In terms of this structure, the composite topologies representing the composite region in the k-tuple ensure that the frontier prime elements are consecutive in the sequence of prime …