| Lucas_Sequences_in_Cryptography Focus on their use in primality testing, with pseudo-code. Includes an explanation of the strong Lucas PRP test. |
| MathWorld__Primality_Testing Articles on many different tests and related subjects. |
| Pseudoprimes/Probable_Primes Papers on primality tests and Frobenius pseudoprimes by Jon Grantham. |
| Behaviour_of_Prime_Numbers An insight into the Goldbach Conjecture. |
| 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 Historical references and links.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. |
GIMPS found two new primes: 243112609-1 (about 12.9 million digits, Aug 08) and 237156667-1 (only 11.1 million digits, Sept 08).
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[ Introduction | Usage
| Technical Specifications | Download ]
Current version:
2.82
Last modified:
Tuesday, 12-Jul-2005 13:28:54 CDT
(This page and the program NewPGen are both written
by Paul Jobling).
Introduction
If you want to quickly find a large prime of the form k.bn+1
or k.bn-1; a large pair of
twin primes,
Sophie
Germain primes, or a Cunningham
Chain of length two; a large BiTwin chain; or a large and long Cunningham
Chain, then the last thing that you should use is Yves Gallot's Proth.exe!
I say the last thing because before that you ought to quickly sieve out
any k, n values that are divisible by small primes. If n
is fixed then this can be done very efficiently, reducing the overall
search time. Another advantage of fixing n is that you can
have a good idea of the overall probability of a successful search.
This program, NewPGen, performs this type of sieving. NewPGen
should be used to throw out candidate k's until the rate at which
it is removing them exceeds the rate at which Proth.exe can perform a
power test. At that point Proth.exe should be used to complete the search, with PMax=0
(as trial factoring has already been performed by NewPGen).
See the Prime Links++ page
on seeking
large primes for related programs (like Proth.exe and PRP).
Usage
To use NewPGen, simply start it up. You can obtain help
from the Help menu item, though it ought to be fairly self-explanatory.
Simple enter the name of the file to generate, the values of the base
and n to use, the range of k to use, the type of sieve to
perform, and press the Start button.
The number of k's that can be sieved is dependent upon available
memory. The more k's that you sieve, the greater the overall
time saved, as more k's are available to be thrown out.
Technical Specifications
NewPGen can currently sieve for the following types of search:
k.bn+1
k.bn-1
k.bn±1 (twin primes)
k.bn-1, 2k.bn-1
(Sophie Germain)
k.2n+1, k.2n+1+3
(Sophie Germain)
k.bn+1, 2k.bn+1
(Cunningham Chain 2nd kind, length 2)
k.bn±1, 2k.bn±1
(BiTwin chain length 1)
k.bn±1, 2k.bn+1
(mixed twin and Cunningham chain)
k.bn±1, 2k.bn-1
(mixed twin and Sophie Germain)
k.bn±1, k.bn+1,
½.k.bn+1 (to test
k.bn+1,
and if that is prime check the other 3 for the chance of a twin prime
or CC 2nd kind)
k.bn±1, 2k.bn-1,
½.k.bn-1(to test
k.bn-1,
and if that is prime check the other 3 for the chance of a twin prime
or Sophie Germain)
Cunningham chains of the first or second kinds of arbitrary length
BiTwin chains of arbitrary length
NewPGen can also be used to generate an output file
to use with some Primeform searches. These are basically the same as the
above, save that a primorial is used:
k.n#+1
k.n#-1
k.n#±1 (twin primes)
k.n#-1, 2.k.n#-1
(Sophie Germain)
k.n#+1, 2.k.n#+1
(Cunningham Chain 2nd kind, length 2)
k.n#±1, 2.k.n#±1
(BiTwin chain length 1)
k.n#±1, 2.k.n#+1
(mixed twin and Cunningham chain)
k.n#±1, 2.k.n#-1
(mixed twin and Sophie Germain)
k.n#±1, ½.k.n#+1,2.k.n#+1
(to test k.n#+1, and if that is prime check
the other 3 for the chance of a twin prime or CC 2nd kind)
k.n#±1, ½.k.n#-1,2.k.n#-1
(to test k.n#+1, and if that is prime check the other 3 for
the chance of a twin prime or Sophie Germain)
Cunningham chains of the first or second kinds of arbitrary length
BiTwin chains of arbitrary length
The maximum candidate divisor for the k.2n
sieves is: 1,152,921,504,606,846,976.
The maximum candidate divisor for the other sieves is: 140,737,488,355,327.
The maximum value of n that can be used in a primorial sieve is:
274,579.
To download, choose one of the following:
Windows Version:
zipped (size
74K
, last updated:
Tuesday, 12-Jul-2005 13:28:54 CDT
)
Linux Version
dynamically linked (size
111K
, last updated:
Monday, 29-Oct-2007 12:00:39 CDT
) or
statically linked (size
463K
, last updated:
Monday, 29-Oct-2007 12:00:43 CDT
)
Another prime page by
Chris K. Caldwell <caldwell@utm.edu>
