The first two consecutive numbers to have two distinct prime factors are:
14 = 2 x 7
15 = 3 x 5
The first three consecutive numbers to have three distinct prime factors are:
644 = 2² x 7 x 23
645 = 3 x 5 x 43
646 = 2 x 17 x 19
Find the first four consecutive integers to have four distinct primes factors. What is the first of these numbers?
let hasDivisor(n) = let upperBound = bigint(sqrt(double(n))) [2I..upperBound] |> Seq.exists (fun x -> n % x = 0I) let isPrime(n) = if n = 1I then false else not(hasDivisor(n)) let naturalNumbers = Seq.unfold (fun state -> Some(state, state+1I)) 1I // define the sequence of prime numbers let primeSeq = naturalNumbers |> Seq.filter isPrime |> Seq.cache // recursive function to find the prime denominators for a number n let rec getPrimeFactors denominators n = if n = 1I then denominators else let denominator = primeSeq |> Seq.filter (fun x -> n % x = 0I) |> Seq.head getPrimeFactors (denominators @ [denominator]) (n/denominator) // curry the getPrimeDenominators function to start with an empty list let primeFactors = getPrimeFactors  // function to get the number of distinct prime factors a number has let distinctPrimeFactorsCount n = primeFactors n |> Seq.distinct |> Seq.length // define the sequence of numbers with exactly 4 distinct prime factors let seq = naturalNumbers |> Seq.filter (fun n -> distinctPrimeFactorsCount n = 4) |> Seq.cache let answer = seq |> Seq.windowed 4 |> Seq.filter (fun l -> Seq.max (l) - Seq.min (l) = 3I) |> Seq.head |> Seq.head
Whilst on the surface this isn’t a very difficult problem to solve, the biggest challenge I had was in making sure the solution runs in a reasonable time hence note the various places where I used Seq.cache to help improve the performance of this code.
I specialise in rapidly transitioning teams to serverless and building production-ready services on AWS.
Are you struggling with serverless or need guidance on best practices? Do you want someone to review your architecture and help you avoid costly mistakes down the line? Whatever the case, I’m here to help.
Check out my new course, Complete Guide to AWS Step Functions. 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, callbacks, nested workflows, 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