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, …

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 …

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

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 …

Jun 22, 2021 · Find consecutive composite numbers [duplicate] Ask Question Asked 4 years, 5 months ago Modified 4 years, 5 months ago

Jan 12, 2021 · @Baropryl In both of your examples, you construct your consecutive numbers such that the smaller of the two is the even number. You must explicitly consider the case that …

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 …

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 …

Since they are consecutive, one is even and the other is odd. Now, squaring the even number is multiplying it an even number of times, so the answer is even. Squaring the odd number, …