You can become a serverless blackbelt. Enrol to my 4-week online workshop Production-Ready Serverless and gain hands-on experience building something from scratch using serverless technologies. At the end of the workshop, you should have a broader view of the challenges you will face as your serverless architecture matures and expands. You should also have a firm grasp on when serverless is a good fit for your system as well as common pitfalls you need to avoid. Sign up now and get 15% discount with the code yanprs15!
It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
9 = 7 + 2×12
15 = 7 + 2×22
21 = 3 + 2×32
25 = 7 + 2×32
27 = 19 + 2×22
33 = 31 + 2×12
It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
let hasDivisor(n) = let upperBound = int64(sqrt(double(n))) [2L..upperBound] |> Seq.exists (fun x -> n % x = 0L) // need to consider negative values let isPrime(n) = if n <= 1L then false else not(hasDivisor(n)) // generate the sequence of odd composite numbers let oddCompositeNumbers = Seq.unfold (fun state -> Some(state, state+2L)) 9L |> Seq.filter (fun n -> not(isPrime n)) // generate the sequence of prime numbers let primeNumbers = Seq.unfold (fun state -> Some(state, state+2L)) 1L |> Seq.filter isPrime // function to check if a number can be written as the sum of a prime and twice a square let isSum(number) = primeNumbers |> Seq.takeWhile (fun n -> n < number) |> Seq.exists (fun n -> sqrt(double((number-n)/2L)) % 1.0 = 0.0) let answer = oddCompositeNumbers |> Seq.filter (fun n -> not(isSum(n))) |> Seq.head
All pretty straight forward here, the only slightly confusing part of this solution is how to determine if a number can be written as the sum of a prime and twice a square:
Odd Composite Number = Prime + 2 x n2 => n = sqrt((Odd Composite Number – Prime) / 2)
As you know Math.Sqrt works with a double and returns a double, hence to find out if n above is a whole number I had to check whether it divides by 1 evenly
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