You can become a serverless blackbelt. Enrol in my course Learn you some Lambda best practice for great good! and learn best practices for performance, cost, security, resilience, observability and scalability. By the end of this course, you should be able to make informed decisions on which AWS service to use with Lambda and how to build highly scalable, resilient and cost efficient serverless applications.
By replacing the 1st digit of *3, it turns out that six of the nine possible values: 13, 23, 43, 53, 73, and 83, are all prime.
By replacing the 3rd and 4th digits of 56**3 with the same digit, this 5-digit number is the first example having seven primes among the ten generated numbers, yielding the family: 56003, 56113, 56333, 56443, 56663, 56773, and 56993. Consequently 56003, being the first member of this family, is the smallest prime with this property.
Find the smallest prime which, by replacing part of the number (not necessarily adjacent digits) with the same digit, is part of an eight prime value family.
// generate all prime numbers under <= this max let max = 200000L let mutable primeNumbers = [2L] // only check the prime numbers which are <= the square root of the number n let hasDivisor n = primeNumbers |> Seq.takeWhile (fun n' -> n' <= int64(sqrt(double(n)))) |> Seq.exists (fun n' -> n % n' = 0L) // only check odd numbers <= max let potentialPrimes = Seq.unfold (fun n -> if n > max then None else Some(n, n+2L)) 3L // populate the prime numbers list for n in potentialPrimes do if not(hasDivisor n) then primeNumbers <- primeNumbers @ [n] let isPrime n = if n = 1L then false else not(hasDivisor(n)) // define function to generate combinations of n elements out of the specified list let rec comb n l = match n, l with | 0, _ -> [] | _,  ->  | k, (x::xs) -> List.map ((@) [x]) (comb (k-1) xs) @ comb k xs // define function to find the wild card digits of a n-digit number let getWildCardDigits n = [1..n-1] |> List.collect (fun n' -> comb n' [0..n-1]) // define function to get the new numbers you get by replacing the digits in the // supplied number n with the same digit let replaceDigits (digits:int list) n = let nDigits = n.ToString().ToCharArray() [0..9] |> List.map (fun n' -> List.init nDigits.Length (fun d -> if List.exists (fun d' -> d' = d) digits then n'.ToString() else nDigits.[d].ToString()) |> List.reduce (+)) |> List.map (int64) // define function to find the lists (if any) of prime numbers obtained by replacing // 1 or more digits of the supplied number n with the same digit let F len n = getWildCardDigits (n.ToString().Length) |> List.map (fun l -> replaceDigits l n |> List.filter (fun n' -> n'.ToString().Length = n.ToString().Length && isPrime n')) |> List.filter (fun l -> l.Length >= len) let answer = primeNumbers |> Seq.skipWhile (fun n -> n < 56003L) |> Seq.map (F 8 ) |> Seq.filter (fun l -> l.Length > 0) |> Seq.head |> Seq.map (fun l -> List.min l) |> Seq.min
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 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!
Are you working with Serverless and looking for expert training to level-up your skills? Or are you looking for a solid foundation to start from? Look no further, register for my Production-Ready Serverless workshop to learn how to build production-grade Serverless applications!
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 wrong about serverless and vendor lock-in
- You are thinking about serverless costs all wrong
- Just how expensive is the full AWS SDK?
- Many faced threats to Serverless security
- We can do better than percentile latencies
- 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
- Top 10 Serverless framework best practices