This is a search tool that uses a probabilistic test to generate prime numbers with up to 200 digits. If a rigorous proof of primality is required, the applet generates another algorithm for probable primes with at most 45 digits.
Existence of large prime numbers and primality tests
Target Student Population:
Students in number theory or cryptography classes.
Prerequisite Knowledge or Skills:
The definition of a prime number.
Type of Material:
Reference material, simulation.
Generation of large prime numbers. Primality tests.
Should run in any browser.
Evaluation and Observation
This site uses two different tests to check if certain integer is a prime: probabilistic test and rigorous test. The calculator first generates a probable prime and upon request performs a rigorous primality test (if the number does not exceed 45 digits) using PARI/GP software. If the number has more than 45 digits the applet is supposed run the primality test using an external site with ECPP test.
A page linked to the results screen contains a general description of the tests that are performed containing bibliographic references.
The description of the tests performed can only be accessed as a hyperlink from the results screen and is not clearly labeled. The applet would benefit if this information were presented at the main page of the applet.
Attempts to run the ECPP test on the number with more than 45 digits fail, possibly due to the dead link.
Potential Effectiveness as a Teaching Tool
In a computational number theory class, the numbers produced by the program can be used in the implementation of encryption algorithms and also to test primality checkers etc.
In an elementary class, the list of successive small primes could be used to introduce algorithms such as the sieve of Eratosthenes and also conjectures such as the twin primes conjecture.
This applet has a glossary link that takes the user directly to the search results in the on-line mathematical encyclopedia Wikipedia.
The tool only does the computation; the instructor has to come up with the ideas for class.
Ease of Use for Both Students and Faculty
Easy to use as a number cruncher. The average user can begin using the applet immediately.
All educational and technical documentation should be linked to the main page of the applet.