Classes of prime numbers

Full reptend prime

In number theory, a full reptend prime, full repetend prime, proper prime or long prime in base b is an odd prime number p such that the Fermat quotient (where p does not divide b) gives a cyclic number. Therefore, the base b expansion of repeats the digits of the corresponding cyclic number infinitely, as does that of with rotation of the digits for any a between 1 and p − 1. The cyclic number corresponding to prime p will possess p − 1 digits if and only if p is a full reptend prime. That is, the multiplicative order ordp b = p − 1, which is equivalent to b being a primitive root modulo p. The term "long prime" was used by John Conway and Richard Guy in their Book of Numbers. Confusingly, Sloane's OEIS refers to these primes as "cyclic numbers". (Wikipedia).

Video thumbnail

The Reciprocals of Primes - Numberphile

Matt Parker explores the work of William Shanks - and boots up the ShanksBot. More links & stuff in full description below ↓↓↓ Matt Parker's 2022 Pi Day Video: https://youtu.be/dtiLxLrzjOQ Discussing William Shanks on Objectivity: https://youtu.be/7yTXMeiVBCc Prime Number playlist: https

From playlist Matt Parker (standupmaths) on Numberphile

Video thumbnail

Stirring the Mandelbrot Set

http://code.google.com/p/mandelstir/

From playlist mandelstir

Video thumbnail

Very Large Primes and (Almost) Perfect Numbers -- MegaFavNumbers

This is my video submission for the #MegaFavNumbers celebration. As promised in the video, here is the very large number that was simply too big for the screen: 5282945208034002678497845769960721106385426547566030332928651387255812371024044147692699871010305634389030253300042369944654409

From playlist MegaFavNumbers

Video thumbnail

2014 GED Exam Math Overview and Prep

GEDmathlessons.com http://www.gedmathlessons.com helps students practice and study for ged math. This video goes over the 2014 GED math requirement and how to study for the exam.

From playlist GED Prep Videos

Video thumbnail

ASVAB exam preparation made easy!

For complete ASVAB exam preparation, visit: https://www.studypug.com/asvab-test-prep

From playlist ASVAB Exam Prep

Video thumbnail

MegaFavNumbers: Plus One Primes, 154,641,337, and 62,784,382,823

My entry in the #MegaFavNumbers series looks at a particularly striking example of a very specific family of primes -- and how it connects to what digits can be the final digit of primes in different bases.

From playlist MegaFavNumbers

Video thumbnail

Schnitt einer Ebene mit einer Geraden

Quickstart für die Desktop Version Beispiel 5: Schnitt einer Ebene mit einer Geraden

From playlist Quickstart für die Desktop Version

Video thumbnail

1,010,010,101,000,011 - #MegaFavNumbers

This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo

From playlist MegaFavNumbers

Video thumbnail

Calculations with Matrix groups over the integers by Alexander Hulpke

DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra

From playlist Group Theory and Computational Methods

Video thumbnail

Why do prime numbers make these spirals? | Dirichlet’s theorem, pi approximations, and more

A curious pattern, approximations for pi, and prime distributions. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/spiral-thanks Based on this Math

From playlist Neat proofs/perspectives

Video thumbnail

Compressed Sensing and Dynamic Mode Decomposition

This video illustrates how to leverage compressed sensing to compute the dynamic mode decomposition (DMD) from under-sampled or compressed data. From the Paper: Compressed Sensing and Dynamic Mode Decomposition. JCD 2(2):165—191, 2015. Steven L. Brunton, Joshua L. Proctor, Jonathan H.

From playlist Research Abstracts from Brunton Lab

Video thumbnail

Crazy product rule proof

In this video, I give a neat proof of the product rule by using the Fourier transform. It’s really neat and natural! Enjoy! Classical product rule proof: https://youtu.be/2uT1IUS_V_4 Cool product rule proof: https://youtu.be/ISSLG4-2LXI Subscribe to my channel: https://www.youtube.com/c

From playlist Real Analysis

Video thumbnail

Local-global compatibility at primes dividing l - David Geraghty

David Geraghty Princeton University/Member, School of Mathematics March 23, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

The Eisenstein Ideal and its Application to W. Stein’s Conjecture....by Kenneth A. Ribet

Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou

From playlist Recent Developments Around P-adic Modular Forms (Online)

Video thumbnail

Multiple Linear Regression (Part D)

Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in

From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics

Video thumbnail

Primes and Primitive Sets (an Erdős Conjecture is cracked) - Numberphile

Extra footage at https://youtu.be/-r2agPNx0gA - Featuring Jared Duker Lichtman. More links & stuff in full description below ↓↓↓ A proof of the Erdős primitive set conjecture: https://arxiv.org/abs/2202.02384 More Prime Number videos: https://bit.ly/PrimePlaylist Jared Duker Lichtman:

From playlist Prime Numbers on Numberphile

Video thumbnail

Álvaro Lozano-Robledo: Recent progress in the classification of torsion subgroups of...

Abstract: This talk will be a survey of recent results and methods used in the classification of torsion subgroups of elliptic curves over finite and infinite extensions of the rationals, and over function fields. Recording during the meeting "Diophantine Geometry" the May 22, 2018 at th

From playlist Math Talks

Video thumbnail

AccuPlacer exam preparation made easy!

For complete AccuPlacer exam preparation, visit: https://www.studypug.com/accuplacer-test-prep

From playlist AccuPlacer Exam Prep

Related pages

Perfect power | Artin's conjecture on primitive roots | Richard K. Guy | If and only if | Primitive root modulo n | Quadratic residue | Conjecture | John Horton Conway | Fermat quotient | Diehard tests | Cyclic number | Multiplicative order | Natural number | Safe prime | Integer | Modulo operation | Divisor | Algebraic number theory | Number theory | Repeating decimal | Prime number | Radix | Parity (mathematics) | Decimal | Square number | Modular arithmetic | Duodecimal