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
Longest known sequence of identical consecutive Collatz sequence . . . I have found a sequence of 67,108,863 consecutive numbers that all have the same Collatz length (height) These numbers are in the range $ [2^ {1812}+1, 2^ {1812}+2^ {26}-1]$ and I believe it is the longest such sequence known to date Also I believe that we can obtain arbitrarily long such sequences if we start from numbers of the form $2^n+1$ I would be very interested to see a proof of
$100$ 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
Probability - consecutive numbers - Mathematics Stack Exchange 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 $^{30}C_3$ Howe
Expected number of consecutive heads in 10 coin tosses I am having trouble formulating the exact recursive relation for this problem The problem statement is A coin is tossed 10 times and the output written as a string What is the expected number of