A Data Science Central Community

I recently posted an article featuring a non traditional approach to find large prime numbers. The research section of this article offers interesting challenges, both for data scientists interested in mathematics, and for mathematicians interested in data science and big data. My approach is data, pattern recognition, and machine learning heavy. Here is the introduction:

Large prime numbers have been a topic of considerable research, for its own mathematical beauty, as well as to develop more powerful cryptographic applications and random number generators. In this article, we show how big data, statistical science (more specifically, pattern recognition) and the use of new efficient, distributed algorithms, could lead to an original research path to discover large primes. Here we also discuss new mathematical conjectures related to our methodology.

Much of the focus so far has been on discovering raw large primes: Any time a new one, bigger than all predecessors, is found, it gets a lot of attention even beyond the mathematical community. Here we explore a different path: finding numbers (usually not primes) that have a very large prime factor. In short, we are looking for special integer-valued functions f(n) such that f(n) has a prime factor bigger than n, hopefully much bigger than n, for most values of n.

*Source for picture: click here*

The distribution of the largest prime factor has been studied extensively. If we choose a function that grows fast enough, one would expect that the largest prime factor of f(n) will always be larger than n. However, this would lead to intractable factoring issues to find the large primes in question. So in practice, we are interested in functions f(n) that do not grow too fast. The problem is that many, if not most very large integers, are friable : their largest prime factor is a relatively small prime. I like to call them porous numbers. So the challenge is to find a function f(n) that is not growing too fast, and that somehow produces very few friable numbers as n becomes extremely large. Read the full article here.

*For another interesting challenge, read the section "Potential Areas of Research" in my article How to detect if numbers are random or not. For other articles featuring difficult mathematical problems, click here. For a statistical problem with several potential applications (clustering, data reduction) click here and read the last section. More challenges can be found here.* .

© 2019 AnalyticBridge.com is a subsidiary and dedicated channel of Data Science Central LLC Powered by

Badges | Report an Issue | Privacy Policy | Terms of Service

**Most Popular Content on DSC**

To not miss this type of content in the future, subscribe to our newsletter.

**Technical**

- Free Books and Resources for DSC Members
- Learn Machine Learning Coding Basics in a weekend
- New Machine Learning Cheat Sheet | Old one
- Advanced Machine Learning with Basic Excel
- 12 Algorithms Every Data Scientist Should Know
- Hitchhiker's Guide to Data Science, Machine Learning, R, Python
- Visualizations: Comparing Tableau, SPSS, R, Excel, Matlab, JS, Pyth...
- How to Automatically Determine the Number of Clusters in your Data
- New Perspectives on Statistical Distributions and Deep Learning
- Fascinating New Results in the Theory of Randomness
- Long-range Correlations in Time Series: Modeling, Testing, Case Study
- Fast Combinatorial Feature Selection with New Definition of Predict...
- 10 types of regressions. Which one to use?
- 40 Techniques Used by Data Scientists
- 15 Deep Learning Tutorials
- R: a survival guide to data science with R

**Non Technical**

- Advanced Analytic Platforms - Incumbents Fall - Challengers Rise
- Difference between ML, Data Science, AI, Deep Learning, and Statistics
- How to Become a Data Scientist - On your own
- 16 analytic disciplines compared to data science
- Six categories of Data Scientists
- 21 data science systems used by Amazon to operate its business
- 24 Uses of Statistical Modeling
- 33 unusual problems that can be solved with data science
- 22 Differences Between Junior and Senior Data Scientists
- Why You Should be a Data Science Generalist - and How to Become One
- Becoming a Billionaire Data Scientist vs Struggling to Get a $100k Job
- Why do people with no experience want to become data scientists?

**Articles from top bloggers**

- Kirk Borne | Stephanie Glen | Vincent Granville
- Ajit Jaokar | Ronald van Loon | Bernard Marr
- Steve Miller | Bill Schmarzo | Bill Vorhies

**Other popular resources**

- Comprehensive Repository of Data Science and ML Resources
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- 100 Data Science Interview Questions and Answers
- Cheat Sheets | Curated Articles | Search | Jobs | Courses
- Post a Blog | Forum Questions | Books | Salaries | News

**Archives**: 2008-2014 | 2015-2016 | 2017-2019 | Book 1 | Book 2 | More

**Most popular articles**

- Free Book and Resources for DSC Members
- New Perspectives on Statistical Distributions and Deep Learning
- Time series, Growth Modeling and Data Science Wizardy
- Statistical Concepts Explained in Simple English
- Machine Learning Concepts Explained in One Picture
- Comprehensive Repository of Data Science and ML Resources
- Advanced Machine Learning with Basic Excel
- Difference between ML, Data Science, AI, Deep Learning, and Statistics
- Selected Business Analytics, Data Science and ML articles
- How to Automatically Determine the Number of Clusters in your Data
- Fascinating New Results in the Theory of Randomness
- Hire a Data Scientist | Search DSC | Find a Job
- Post a Blog | Forum Questions

## You need to be a member of AnalyticBridge to add comments!

Join AnalyticBridge