# I’m trying to find the longest consecutive set of composite numbers

Hello and I’m quite new to Math SE.

I am trying to find the largest consecutive sequence of composite numbers. The largest I know is:

I can’t make this series any longer because $97$ is prime unfortunately.

I can however, see a certain relation, if suppose we take the numbers like (let $a_1, a_2, a_3,...,a_n$denote digits and not multiplication):

The entire list of consecutive natural numbers I showed above can be made composite if:

1. The number formed by digits $a_1a_2a_3...a_n$ should be a multiple of 3
2. The numbers $a_1a_2a_3...a_n1$ and $a_1a_2a_3...a_n7$ should be composite numbers

If I didn’t clearly convey what I’m trying to say, I mean like, say I want the two numbers (eg: ($121$, $127$) or ($151$, $157$) or ($181$, $187$)) to be both composite.

I’m still quite not equipped with enough knowledge to identify if a random large number is prime or not, so I believe you guys at Math SE can help me out.

## Answer

You can have a sequence as long as you wish. Consider $n\in\Bbb{N}$ then the set

is made of composite consecutive numbers and is of length $n-1$

Attribution
Source : Link , Question Author : Pritt Balagopal , Answer Author : marwalix