By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10001st prime number?
open System let findFactorsOf(n) = let upperBound = int32(Math.Sqrt(double(n))) [2..upperBound] |> Seq.filter (fun x -> n % x = 0) let isPrime(n) = findFactorsOf(n) |> Seq.length = 0 let primeNumbers = Seq.unfold (fun x -> Some(x, x + 1)) 2 |> Seq.filter isPrime let p = primeNumbers |> Seq.nth(10000)
Here I borrowed the findFactors and isPrime functions I first used in the problem 3 solution, except this time they don’t have to be constrained to work int64 types.
The rest of the solution’s pretty straight forward too, to find the 10001st prime number I first need to generate the sequence of all prime numbers. I did so by using Seq.unfold to generate the list of all natural numbers equal or greater than 2 (the first prime number), coupled with the isPrime predicate:
let primeNumbers = Seq.unfold (fun x -> Some(x, x + 1)) 2 |> Seq.filter isPrime
With the sequence of all prime numbers at hand, Seq.nth is used to find the element at the index position 10000 (sequences are zero-indexed like arrays, so this is actually the 10001st element in the sequence) to get our answer!
Enjoy what you’re reading? Subscribe to my newsletter and get more content on AWS and serverless technologies delivered straight to your inbox.
I’m an AWS Serverless Hero and the author of Production-Ready Serverless. I have run production workload at scale in AWS for nearly 10 years and I have been an architect or principal engineer with a variety of industries ranging from banking, e-commerce, sports streaming to mobile gaming. I currently work as an independent consultant focused on AWS and serverless.
In this course, we’ll cover everything you need to know to use AWS Step Functions service effectively. Including basic concepts, HTTP and event triggers, activities, design patterns and best practices.
Here is a complete list of all my posts on serverless and AWS Lambda. In the meantime, here are a few of my most popular blog posts.
- Lambda optimization tip – enable HTTP keep-alive
- You are thinking about serverless costs all wrong
- Many faced threats to Serverless security
- We can do better than percentile latencies
- I’m afraid you’re thinking about AWS Lambda cold starts all wrong
- Yubl’s road to Serverless
- AWS Lambda – should you have few monolithic functions or many single-purposed functions?
- AWS Lambda – compare coldstart time with different languages, memory and code sizes
- Guys, we’re doing pagination wrong