- 23 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Mersenne Numbers, Strings, the Rule of 6, and the Method of Fractions
About this book
Academic Paper from the year 2023 in the subject Mathematics - Analysis, grade: 2.00, , language: English, abstract: The work developed here brings a significant measure of order to the search for prime numbers.
It is shown conclusively that no Mersenne number can have an integer square root, this being, until now, one of the unsolved problems in Number theory. It is shown that there are a new set of numbers given by F = (M + 2)/3 where M is a Mersenne number. it is found that when M is prime then F is prime. however, it is also found that prime numbers may be generated when M is composite and the index of the Mersenne number is prime, but this is not invariably the case.
An accelerated method of trial division is derived and from which we construct one row matrices which we have called, templates. These are found to be of great utility in determining factors of numbers, and their 'extent' is equal to the number of digits in a number of interest. The template may be easily extended by a simple process explained in the text. Extension of a template by one unit increases that range of numbers which may be examined by an order of magnitude.
Information
Table of contents
Trusted by 375,005 students
Access to over 1.5 million titles for a fair monthly price.
Study more efficiently using our study tools.
Frequently asked questions
Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription
No, books cannot be downloaded as external files, such as PDFs, for use outside of Perlego. However, you can download books within the Perlego app for offline reading on mobile or tablet. Learn how to download books offline
Perlego offers two plans: Essential and Complete
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.5M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1.5 million books across 990+ topics, we’ve got you covered! Learn about our mission
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more about Read Aloud
Yes! You can use the Perlego app on both iOS and Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app
Yes, you can access Mersenne Numbers, Strings, the Rule of 6, and the Method of Fractions by William Fidler in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over 1.5 million books available in our catalogue for you to explore.