Generate arbitrarily long sequences of consecutive numbers …
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 …
Consecutive composite numbers - Mathematics Stack Exchange
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, …
probability - What is the expected number of times a dice has to …
Basically, on average, how many times one should roll to expect two consecutive sixes?
I'm trying to find the longest consecutive set of composite numbers
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 …
Proof: Sequence of n consecutive natural numbers containing no …
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
The product of $n$ consecutive integers is divisible by $n$ factorial
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 …
$100$ consecutive natural numbers with no primes
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 …
Probability - consecutive numbers - Mathematics Stack Exchange
Sep 4, 2015 · Question: Three numbers are selected out of the first 30 natural numbers. What is the probability that none of them are consecutive? I know that the total possibilities will be …
Counting bit strings of length 10 contain either 5 consecutive 0's …
Jan 24, 2015 · We need to subtract out the double counted 6 (+)-consecutive cases of which there are $5\cdot 2^4$ by the same logic. The 6-consecutive-zero strings also overcount, but in any …
algebra precalculus - Proving the product of four consecutive …
Jun 27, 2018 · Assume $m$ is the product of four consecutive integers. If $m$ is the product of four consecutive integers, then write $m=x (x+1) (x+2) (x+3)$ where $x$ is an integer.