# About project

## About Wieferich@home

Wieferich@home is a scientific experiment that uses Internet-connected computers in the Search for next Wieferich and Near-Wieferich primes. You can participate by running a free application or screensaver that seeks Wieferich primes. Application has implemented optimal algorithms for systematic seeking the next Wieferich prime. Wieferich@home is a screen-saver or application that uses your computer's idle time to seek Wieferich primes. We want to find the third Wieferich prime and new Near-Wieferich primes. Help scientists to search the third Wieferich prime and participate.

## What is Wieferich prime

Wieferich primes **1093, 3511** was found by Mr. W. Meissner in 1913 and N. G. W. H. Beeger in 1922. properties of Wieferich primes you can read over here. There are tests by means of optimal algorithms and procedures next new candidates with use of all information of about two's known W. primes and their properties.

## How does Wieferich@Home work

When you run Wieferich@Home - application on your PC, it works as follows (see below):

- After application's first start will be require simply member registration.
- Your PC downloads units for computing. Units are decoded and verified and send to complete test's algorithm and periodical test's algorithm.
- If there are founded Wieferich primes or Near-Wieferich primes, they are saved to the temporary results store.
- Your PC uploads completed units to the data server and verify by MD5 hash algorithm.
- Your PC loads results from the results store and results are encrypted by RSA algorithm and report to the scheduling server. After succesfull verification are downloaded new units for next work.
- If received unit is O.K., member gets one points and application download increased member's score. This cycle is repeated indefinitely.

When you run Wieferich@Home - screensaver, it works as follows (see below):

Screensaver doesn't require member registration, but screen-saver communicate with server with fixed member's name `screensaver`, which was created special for processing units in Wieferich@Home - screensaver. Software works with same seeking algorithms and gets same possible results. Seeking speed of both applications is similar.

**Another numbers (2 - 5)**are same as in Wieferich@Home - application.

## How does application work

Diagram software of Wieferich@Home - application or screensaver you can see below:

Application contains two seeking algorithms i. e. algorithm of complete test (CTA) and algorithm of periodical test (PTA). CT algorithm test each successive prime - number for Wieferich prime or Near- Wieferich prime. There was specified seeking start value 1170553064286511. CT Algorithm processes CT-unit, that contains always the same size of seeking range (1 000 000 000). PT algorithm works with periodical strings, which are combining by given binary periods. PT algorithm works with very interesting bit's length of periodical binary numbers as late as 3500 bits. Every received PT-unit contains always 150 different periods for processing. Both algorithms run in parallel application's thread with same lowest CPU usuage! If there're founded some results (Wieferich or Near-Wieferich primes), they are encrypted and saved to the results store. After completing unit is sending entire contents of the results store on this server. Each of results will be present here on www.elmath.org. Dispatcher (the third application's thread) does member's registration, verification of received (sended) units, prepares units to the PT and CT algorithm, sends results from the results store. All data files and communication with server are protected by MD5 Hashing. Results saved to the results store are encoded by RSA algorithm. Any unauthorized file's modification causes break files and software will repare them.