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, \\quad 2 \\leq
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 that "does not use the properties of binomial coefficients"
$100$ consecutive natural numbers with no primes 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
Im trying to find the longest consecutive set of composite numbers 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 numbers, and therefore form an intersection of similarly translated composite topologies