| Christian_Goldbach Biography, with links to other Goldbach resources. |
| An_\"Expository_Proof\"_of_the_Goldbach_Conjecture An elementary attack on the problem of prime sums. |
| Goldbach_Conjecture Article from MathWorld. |
| The_Goldbach_Conjecture From the Primes Glossary. Historical references and links. |
| Goldbach_Conjecture_Research Information on research and computations on the Goldbach Conjecture. By Mark Herkommer. |
| Goldbach_Conjecture_Verification Computational results up to 3.10^17 and graphics by Tomás Oliveira e Silva. |
| Goldbach\'s_Conjecture_-_Recent_Progress A summary of some recent progress towards Goldbach's conjecture with references to the literature. |
| Mathematical_Mysteries A brief popular article with an applet generating solutions. |
| Proof_of_the_Twin_Primes_Conjecture Goldbach's Conjecture proves and extends the Twin Primes Conjecture as probable. |
| A_Simple_Solution_to_the_Goldbach_Conjecture A heuristic approach by Piers Newberry. |
| The_Stepladder_Proof_of_The_Goldbach_Conjecture A proposed proof offered for criticism. |
| XGC An eXtension of the Goldbach Conjecture. Mathematica code. |
| Advanced_Placement_Digital_Library_for_Biology,_Physics_and_Chemistry An NSF funded Rice University Digital Library project that hosts free reviewed online resources, linked to the content outline, for AP and Pre-AP teachers and students of biology, physics and chemistr |
| All_Science_Den_com Articles about assorted topics, such as molecular biology, physics. Some include Flash animations to help explain concepts. |
| American_Communications_Foundation_Newsource__Science_&_Technology Assists the commercial broadcast news media in its coverage of science and technology, which is often under-reported because of staffing and budgetary restraints. Enhances the coverage by providing re |
| Animonautes Production of 3D media to offer learning experiences in medicine, biology, astronomy and technology. Page includes sample videos. |
| ANOVA_Science_Education Services public and private school districts and schools on the continental USA and in Hawaii through teacher and administrator seminars and workshops. |
| Asia_Link_program__MUMA_project A training project dedicated to improve the quality of higher education for heritage management in Asia and Europe. The project runs from March 2004 to August 2006. |
| Ask_Dr__Jekyl_and_Mr__Hyde Answers to a variety of science and technology questions, including questions you never thought to ask. |
| Athena NASA page features earth and space science resources for K-12 and teachers. Included are class exercises with data collecting and background information for each topic, as well as related links. |
| Attaining_Excellence_Through_TIMSS Resources for learning about and discussing the Third International Mathematics and Science Study, including related reports, data and commentaries. |
| BBC_Science_&_Nature Information about humans, animals, space, the planet Earth and various hot topics. Includes TV listings, Listen Again online radio, news reports, quizzes, picture galleries and games. |
| Berkshire_Biological_Supply_Company Online sale of living organisms for biology class, science fair projects, home teaching. |
| BETR_World_Science_and_Computer_Education Offering information on classes and camps for science and computer education in Maryland and Virginia. |
| Beyond_Discovery A series of articles that trace the origins of important recent technological and medical advances. Each story reveals the crucial role played by basic science. |
| Bill_Nye_the_Science_Guy Online science laboratory. Includes learning activities and show information. |
| Brainium A curriculum-based, online environment where teachers and students can share ideas, experiments and activities. |
| The_Bubblesphere All about soap bubbles. Bubble blowing, solutions, history, fun, Java games, bubble machines and trivia. |
| Candis_Mitchell\'s_Science_Teacher\'s_Site Designed to help educators search for internet material appropriate for their classrooms. |
| Cornell_Theory_Center_Math/Science_Gateway Links to resources in mathematics and science for educators and students in grades 9-12. |
| Cute_Science Learning materials for include coloring books, audio lectures, videos and workbooks. Subjects covered are math, science, and HTML. Includes product list and online order form. |
| Department_of_Energy_Science_Education_Programs Internship and fellowship opportunities for undergraduate students and teachers related to science, technology, engineering, and mathematics. |
| Did_You_Ever_Wonder? Each month a dozen questions are posed and answered by lab scientists on various topics on how things work in the natural world. |
| Dive_and_Discover__Expeditions_to_the_Seafloor An interactive distance learning web site designed to immerse your students in the exciting process of deep-sea research and exploration. |
| Dr__Carlson\'s_Science_Theater Video podcast of cool science demonstrations. |
| Dr__Fred\'s_Place Children's science author, Dr. Fred Bortz, including biographical information, list of books, FAQ's, and information about school visits. |
| Ed_Quest Includes guided links for students, lesson plans and references for teachers, as well as collaborative projects directed towards the middle school level. |
| Education_Links_-_Top_rated_educational_sites_ Collection of educational resources separated into categories such as astronomy, lesson plans, math, and webquests. |
| Educational_Resources_Catalog In addition to the catalog itself, links are provided to curriculum materials, professional development, software, visual and audiovisual classroom support, print material and online resources. |
| Elementary_Science_Program Includes activity of the month for students and teachers of elementary science, as well as an archive of past activities, and resources. |
GIMPS found two new primes: 243112609-1 (about 12.9 million digits, Aug 08) and 237156667-1 (only 11.1 million digits, Sept 08).
Home
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[ Download | Submit Primes | Ranges
& Projects | Related Programs | Search
Database ]
Current version:
7.1
Program last modified:
Tuesday, 12-Jul-2005 13:28:52 CDT
Introduction
Originally, Yves Gallot wrote a program to implement the following theorem
from our pages on primality proving
(page three):
Proth's Theorem (1878): Let N = k.2n+1
with 2n > k. If there is an integer
a such that
a(N-1)/2 = -1 (mod
N),
then N is prime.
This test is so simple that in practice the difficulty is quickly
multiplying the large numbers involved. It is also a very useful test:
it applies to Cullen
primes, Fermat
factors, the primes in the Sierpinski
conjecture... (See Ray Ballinger's Proth
Range Page for additional information.)
Yves Gallot
has now expanded this program to also cover prime of the form k.2n-1!
His "Proth.exe" program makes finding all these types of primes
as easy as selecting the form you desire from a menu, choosing the starting
values (here Ray Ballinger's Proth
Range page's are especially helpful) and then letting the machine
go. Big primes take awhile to find, so Yves programs tracks where it is
and can automatically continue each time you start your machine. You can
adjust the priority of the program so it only runs when your machines
is doing nothing else...
Other features include the ability to set a range for the starting k
(odd) and n, to set certain algebraic forms for the multiplier,
and to test (automatically) if any prime you find is part of a twin
prime or Sophie
Germain prime pair...
To download, choose one of the following:
Download
Program (size
380K
, last updated:
Tuesday, 12-Jul-2005 13:28:52 CDT
)
(or download
pkzipped version,
181K
last updated:
Tuesday, 12-Jul-2005 13:28:53 CDT
)
Ranges to search & Projects to join
Joe DeMaio's Generalized
Woodall number search.
Ray Ballinger's Proth
Range Page's contains pages for coordinating the searches for Cullen
primes, Woodall primes, "Proth" primes and the Sierpinski
problem.
Yves Gallot's Generalized
Fermat Prime Search--Proth.exe is faster when used on this type
of prime.
Related pages
Paul Jobling's NewPGen which can be used
to pre-sieve candidates for Prothe.exe searches.
George Woltman's PRP
can be used to take the output of NewPGen, apply a prp test, then create
a file for Proth.exe to prove. Get prp.zip for Windows and
prp.tgz for Linux on an Intel *86 processor.
Chris Nash's PrimeForm
- built with the same arithmetic library as Proth.exe, PrimeForm allows
much move variety in the form of the prime numbers sought.
Andy Penrose's Proth
benchmarks for various machines
See also the Prime Links++ programs
directory.
When you find a new prime:
At this site we keep database of the 5000 Largest
Known Primes, plus the
top twenty of certain special forms (Cullen, twin,...) If you find
any primes that would fit on this list, please let me know! To see
what is already on the list, you can use the search
engine below.
Search the list for primes of these forms
Search Database of the Largest Known Primes
for primes of the form: k.bn+/-1
Limit on multiplier k
(leave blank for no limit)
minimum
maximum
Limit on exponent n
(leave blank for no limit)
minimum
maximum
Base b
base
Which sign(s)?
plus
minus
Find at most
number
(other
searches)
Click here for other ways to
search at this site and in this database.
Another prime page by
Chris K. Caldwell <caldwell@utm.edu>
