A Prime Seminar on Primes Notes

Abstract

Video: Purdue Math Club:
Prime Seminar on Primes:
March 21, 2012

Powerpoint Presentation

Please don't change this Powerpoint without my permission.

Videos in order

#1 (Slide 2): Warner Bros.: The Brain (From "Pinky and The Brain" or "Animaniacs") Tells A Mathematical Horror Story.
#2 (Slide 2): TheSingingNerd: The Biggest Prime.
#3 (Slide 2): Student CNN News: The Largest Prime Number...So Far.
#4 (Slide 3): The Associated Press: UCLA Researchers Find (Second) Largest Known Prime Number.
#5 (Slide 8: Cuneiform Slide): MADtv - iRACK (including blooper): (Not shown in Matt's final presentation).
#6 (Slide 13): Square One TV - Prime Club: (Not shown in Matt's final presentation).
#7 (Slide 36): Accelerate Your Programming or Science Career with GPU Computing: An Introduction to Using CUDA: (Not shown in Matt's final presentation) (The parts that I mentioned with facial recognition and mosquitoes getting shot with lasers are from about 48:10 to about 51:00).
#8 (Slide 36): CUDA 5 and Beyond: (Not shown in Matt's final presentation).
#9 (Mentioned only): Mathematician Erastosthenes is in Carl Sagan's Cosmos Episode 1 from about 31:00 to about 36:50.

Numbers tested in Alpertron in The Presentation

It probably doesn't matter much, but I put in the maximum number of digits in a group, and put checks next to "Verbose mode" & "Use Cunningham tables on server."
(10^499)^2+(10^499)+41 uses (n^2+n+41).
(((10^11-1)/9)*10^20+111*10^14)*(10^(13*20)-1)/((10^20-1)/1)+((10^11-1)/9) is a palindrome.
(10^1031-1)/9 is a repunit and wasn't discovered by Matt.

Scans of support material

Archimedes Myriads of Myriads: Cover, Page 1, Page 2 (206,545-Digit Number)

Bracelet Number: Cover, Page 1, Page 2

Prime Proving Programs:

You can't use decimal points or commas in any of the programs I've used.
OpenPFGW: Sourceforge.net (Last updated on March 25, 2013.) or Yahoo Group.
PrimeForm: (Normally not used anymore).
Alpertron Elliptical Curve Method Factorization Applet: It tests for factors of numbers up to 9,332 digits. You need Java and Mozilla Firefox or Google Chrome from CNET. For some reason, The ECM Applet doesn't always work in Internet Explorer.
NewPGen: (Sieve of Erastostheses).
Proth: I don't use it much, but I understand that it's used to find Generalized Fermats. There are more Generalized Fermats than any type on Chris Caldwell's Top 5000 Lists.
PRIMO: The Windows version is no longer updated.
You might check out MATlab, Mathematica, and Wolfram Alpha, but I don't know very much about them.
...and if there are any that I'm forgetting.
There are also programs that aren't released to the public.

Factoring Programs

GGNFS
Alpertron: Elliptical Curve Method Factorization Applet
Y.A.F.U.: Yet Another Factorization Utility
ECMNET
PRIMO
I can't help you much with factoring programs because I don't know that much.

If a program won't download, then contact me.

Some Project Web Pages

G.I.M.P.S.: Great Internet Mersenne Prime Search (I don't recommend because it takes too long), FAQ.
Repunit Project (I do recommend.)
BiTwin Project
Makoto Kamada's Repunit Factoring Project: Page 1 & Page 2.
Fibonacci Project: There's a 411,439-digit Fibonacci probable prime at Probable Primes. Email Henry Lifchitz if you are interested in searching for a Fibonacci probable prime using a sieve program.
Seventeen or Bust
Double Mersenne (Finding a Factor)
Operation Billion Digits (Factoring)
Contact bigprimes.net to see if they have a project that you'd be interested in.
Factors of Googolplex Plus Power of Ten Project: Source or Windows.
Factors Of Numbers Near Googolplex Plus Project: Source or Windows.
Factors Of Numbers Near Googolplex Minus Project: Source or Windows.
Factors Of Numbers Near Googolplexplex Plus Project: Source or Windows.
Factors Of Numbers Near Googolplexplex Minus Project: Source or Windows.

Some Distributed Computing Not Related To Primes or Factoring

Distributed Computing .info
S.E.T.I.: Search for Extra Terrestrial Intelligence.

Public Prime Databases

Chris Caldwell's Top 5000 has over 106,000 Probable Primes.
Chris Caldwell's Top 20 Lists
GL Honaker's Prime Curios
The Lifchitz Brothers' Probable Primes has over 94,000 Probable Primes.
Matt Stath's Top Secret Top 50 Primes is under construction. Hopefully it will be updated every month.

Some Prime Generating Formulas Pages

http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
http://www.mersenneforum.org/showthread.php?t=946 (Look at HiddenWarrior's formulas)
http://www.mersenneforum.org/showthread.php?t=6416
http://en.wikipedia.org/wiki/Ulam_spiral
http://en.wikipedia.org/wiki/Formula_for_primes
http://mathworld.wolfram.com/PrimeArithmeticProgression.html
http://primes.utm.edu/glossary/xpage/Illegal.html
http://www.primepuzzles.net/
http://primepatterns.wordpress.com/
http://prime-pattern.com/index.html
Discover Magazine Article: 61: Prime-Time News
Arithmetic Progressions: http://primes.utm.edu/primes/search.php
Consecutive Primes in Arithmetic Progression: http://primes.utm.edu/top20/page.php?id=13
Very Detailed and interesting!: http://www.magic-squares.net/primes.htm

Code for find a near-random digit number

The largest randomly generated prime is 26,642 digits. I don't believe in psychics. Find a randomly generated number with at least 26,642 digits from Psychic Science. My video from : to : shows how to eliminate the spaces. Copy and paste the number and we'll call it randonly_generated_number. This is what you need to type in worktodo.txt:

ABC2 2*$a+1+randonly_generated_number
a: from 0 to 400000000

Or

ABC2 1*$a+1+randonly_generated_number
a: from 0 to 400000000 step 2

Then load it into OpenPFGW. I only know how to use the Windows, not the Macintosh, Unix, or Linux version.
I want to eventually keep a Top 50 List of The 50 near-random primes.
Note: Only include the +1 if it's an even random number.

The Most Massive Numbers in Existence:

Live Science: Biggest Numbers in The Universe.

Hardware

NVIDIA CUDA: It's optional and 6 times faster, but it's expensive. My friend in Germany tests Repunits in NVIDIA CUDA.

Misc

Watch Purdue Engineers, Mitch Daniels parody "Thrift Shop".
If you like Astronomy, Math, and Computers, then watch The Antikythera Mechanism on NOVA on April 3, 2013.
Update on April 5, 2013: I watched The Ancient Computer episode of NOVA (With the full video now at the above link) and itís excellent. They talked about the robotic arms that The Romans believed Archimedes used to pull ships from the water. I had heard of these robotic arms by Archimedes 2 times before, but what I had heard earlier was that they were propaganda by the Romans to make Archimedes look crazy or malicious. Thatís why I said in slides 9 and 10 of my presentation that the 206,545-digit number could have been propaganda by The Romans to make him look crazy.

Last updated on April 5, 2013. You can email stathmk (at) yahoo.com .