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The prime 41, can be written as the sum of six consecutive primes:
41 = 2 + 3 + 5 + 7 + 11 + 13
This is the longest sum of consecutive primes that adds to a prime below one-hundred.
The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.
Which prime, below one-million, can be written as the sum of the most consecutive primes?
// generate all prime numbers under <= this max let max = 10000 // initialise the list with 2 which is the only even number in the sequence let mutable primeNumbers =  // only check the prime numbers which are <= the square root of the number n let hasDivisor n = primeNumbers |> Seq.takeWhile (fun n' -> n' <= int(sqrt(double(n)))) |> Seq.exists (fun n' -> n % n' = 0) // only check odd numbers <= max let potentialPrimes = Seq.unfold (fun n -> if n > max then None else Some(n, n+2)) 3 // populate the prime numbers list for n in potentialPrimes do if not(hasDivisor n) then primeNumbers Seq.filter (fun n' -> n' > n) |> Seq.scan (fun (sum, count) n' -> (sum+n', count+1)) (n, 1) |> Seq.takeWhile (fun (sum, count) -> sum < 1000000) |> Seq.filter (fun (sum, count) -> isPrime sum) |> Seq.maxBy (fun (sum, count) -> count) // for all numbers, find the longest sequence let answer = primeNumbers |> Seq.map getPrimeSequence |> Seq.maxBy (fun (sum, count) -> count)
Again, utilizing the PGsimple 3 algorithm from here, this solution runs in just over a second as I’ve restricted it to check sequences starting with a prime < 10000 which perhaps unsurprisingly, has provided me with the answer.
The only tricky part in this problem is how to build up a list of sequences for each starting prime and find the longest sequence starting from that number which results in a prime < 1000000. Fortunately you can do this rather easily with Seq.scan in F# which works similarly to Seq.fold but gives you all the intermediate results as well as the final result. Used in conjunction with Seq.takeWhile it allows me to get all the sequences which sums up to a number less than 1000000. The rest is pretty straight forward, filter out the sums that aren’t prime numbers and find the longest sequence, and do this for all the primes we have generated to find the answer to the problem.
Hi, I’m Yan. I’m an AWS Serverless Hero and I help companies go faster for less by adopting serverless technologies successfully.
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.
Skill up your serverless game with this hands-on workshop.
My 4-week Production-Ready Serverless online workshop is back!
This course takes you through building a production-ready serverless web application from testing, deployment, security, all the way through to observability. The motivation for this course is to give you hands-on experience building something with serverless technologies while giving you a broader view of the challenges you will face as the architecture matures and expands.
We will start at the basics and give you a firm introduction to Lambda and all the relevant concepts and service features (including the latest announcements in 2020). And then gradually ramping up and cover a wide array of topics such as API security, testing strategies, CI/CD, secret management, and operational best practices for monitoring and troubleshooting.
If you enrol now you can also get 15% OFF with the promo code “yanprs15”.
Check out my new podcast Real-World Serverless where I talk with engineers who are building amazing things with serverless technologies and discuss the real-world use cases and challenges they face. If you’re interested in what people are actually doing with serverless and what it’s really like to be working with serverless day-to-day, then this is the podcast for you.
Check out my new course, Learn you some Lambda best practice for great good! In this course, you will learn best practices for working with AWS Lambda in terms of performance, cost, security, scalability, resilience and observability. We will also cover latest features from re:Invent 2019 such as Provisioned Concurrency and Lambda Destinations. Enrol now and start learning!
Check out my video 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. There is something for everyone from beginners to more advanced users looking for design patterns and best practices. Enrol now and start learning!
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.
- All you need to know about caching for serverless applications
- Lambda optimization tip – enable HTTP keep-alive
- You are wrong about serverless and vendor lock-in
- You are thinking about serverless costs all wrong
- Just how expensive is the full AWS SDK?
- Check-list for going live with API Gateway and Lambda
- How to choose the right API Gateway auth method
- CloudFormation protip: use !Sub instead of !Join
- AWS Lambda – should you have few monolithic functions or many single-purposed functions?
- Guys, we’re doing pagination wrong
- Top 10 Serverless framework best practices
- How to break the “senior engineer” career ceiling
- My advice to junior developers