Search results “Mersenne primes cryptography math”

French monk and math enthusiast Marin Mersenne (1588-1648) was playing around with powers of two and found an interesting possible source of prime numbers from them. The primes that appear from his method are today called Mersenne Primes. In this video we play with them a bit and see when they can occur.

Views: 6052
DrJamesTanton

What is a Mersenne Prime? A guide to finding them, and how you can take part...
VISIT MATHORMATHS.COM FOR MORE LIKE THIS!
Follow me on www.twitter.com/mathormaths, and like www.facebook.com/mathmathsmathematics to stay up to date with tutorials and examination walk throughs. You can always request your own videos!

Views: 10141
MathMathsMathematics

Views: 3418
Eddie Woo

Proving two things:
1. About conditions necessary for there to be a Mersenne Prime (two must be raised to a power of a prime),
2. About Mersenne primes and perfect numbers.

Views: 4643
RandomMathsInc

Views: 6864
Khan Academy Labs

How many prime numbers are there? Will we ever run out? Euclid's proof, elegant and beautiful in how simply and efficiently it deals with such a seemingly enormous problem, settled it once and for all. That's one of the coolest things about maths - once you prove something, it's been proved forever.
This video comes from a series of lessons about cryptography (prime numbers are hugely important to modern encryption algorithms).

Views: 9201
Eddie Woo

Back to School Special. This short series will discuss pseudo random number generators (PRNGs), look at how they work, some algorithms for PRNGs, and how they are used.
Support Coding Math: http://patreon.com/codingmath
Source Code: https://jsbin.com/nifutup/1/edit?js,output
Earlier Source Code: http://github.com/bit101/codingmath

Views: 29494
Coding Math

Random vs. Pseudorandom Number Generators
Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/the-fundamental-theorem-of-arithmetic-1?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/perfect-secrecy?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information).
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Computer Science channel: https://www.youtube.com/channel/UC8uHgAVBOy5h1fDsjQghWCw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 164092
Khan Academy Labs

Views: 13419
Eddie Woo

Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].

Views: 6631
MathDoctorBob

Featuring Matt Parker...
More links & stuff in full description below ↓↓↓
See part one at: https://youtu.be/tlpYjrbujG0
Part three on Numberphile2: https://youtu.be/jNXAMBvYe-Y
Matt's interview with Curtis Cooper: https://youtu.be/q5ozBnrd5Zc
The previous record: https://youtu.be/QSEKzFGpCQs
Mersenne Numbers and Mersenne Primes: https://youtu.be/PLL0mo5rHhk
More on Mersenne Primes: https://youtu.be/T0xKHwQH-4I
GIMPS: http://www.mersenne.org
Prime Playlist: http://bit.ly/primevids
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
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Other merchandise: https://store.dftba.com/collections/numberphile

Views: 1216623
Numberphile

The AKS Test has been a major break-through in the search for Prime Numbers.
More links & stuff in full description below ↓↓↓
See the previous video about Fermat's Prime Test at: http://youtu.be/jbiaz_aHHUQ
The video features Dr James Grime - http://singingbanana.com
The AKS Test paper: http://bit.ly/primetest
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
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Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
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Views: 657724
Numberphile

Paper by Divesh Aggarwal and Antoine Joux and Anupam Prakash and Miklos Santha, presented at Crypto 2018. See https://iacr.org/cryptodb/data/paper.php?pubkey=28795

Views: 100
TheIACR

Finding the biggest prime number might not only have applications in computing, it could also win you some serious money. Here’s how.
The ‘Ham Sandwich Theorem’ Will Change How You See the Universe… Seriously - https://youtu.be/uhNqEs7vDGg
Read More:
How a FedEx employee discovered the world’s largest prime number
https://www.popsci.com/worlds-largest-prime-number-discovered
“Pace first became interested in searching for primes back in 2003, when he read an article about the discovery of the 40th known Mersenne prime— a special kind of prime number, and a rare, numerical creature.”
Largest prime number ever found has over 23 million digits
https://www.newscientist.com/article/2157773-largest-prime-number-ever-found-has-over-23-million-digits/
“The new prime number, known as M77232917, is one million digits larger than the previous record. It is also a particularly rare type of prime called a Mersenne prime, meaning that it is one less than a power of two.”
Welcome to GIMPS, the Great Internet Mersenne Prime Search
https://www.mersenne.org/
“GIMPS was founded in 1996 by George Woltman. The software ran on Intel i386 systems using hand-tuned assembly code for the critical calculations, resulting in highly optimized Lucas-Lehmer code. It wasn't long before GIMPS had its first discovery in November of that same year, showing the effectiveness of distributed computing in harnessing spare computer cycles in a coordinated effort.”
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Seeker explains every aspect of our world through a lens of science, inspiring a new generation of curious minds who want to know how today’s discoveries in science, math, engineering and technology are impacting our lives, and shaping our future. Our stories parse meaning from the noise in a world of rapidly changing information.
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Seeker http://www.seeker.com/

Views: 156090
Seeker

I recommend when you can, to check out
Liar Numbers - Numberphile
https://www.youtube.com/watch?v=jbiaz_aHHUQ&t=16s

Views: 556
Jack T

The following video is a video response to Stefan's (stschmalhaus) "Two Year YouTube Anniversary" giveaway contest. This is by far the most difficult challenge rules that I have ever seen on YouTube. Stefan allows you to pick your poison between 3 challenging video response topics. I am extremely poor at speaking foreign languages and especially French, so Challenge #1 is out for me. After watching "Julie and Julia", I do not feel qualified to properly prepare a typical French cuisine, so Challenge #2 is also out. That leaves Challenge #3, which states the following:
"The French mathematician Marin Mersenne (1588--1648) contributed greatly to number theory. Make an educational video on Mersenne prime numbers, explain what they are, and why mathematicians are fascinated by them. Also, explain the proof of at least one basic theorem about Mersenne primes. The language of the video must be English."
My Two Year YouTube Anniversary Giveaway!
http://www.youtube.com/watch?v=LIBjkEOkr8I&list=UUppuObQHn8alCHGGVESilhA&index=4&feature=plcp
For more information on Mersenne Prime Numbers and to help the mathematics community find the next Mersenne Prime, please visit the "GIMPS" website:
"Great Internet Mersenne Prime Search" (GIMPS)
http://www.mersenne.org/

Views: 3048
TheUrbanPrepper

We group Mersenne numbers into families and notice Mersenne primes tend to exist in the early generations. Grouping Mersenne numbers into families could be a viable strategy in the search of Mersenne primes.

Views: 91
B Ly

This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

Views: 24285
Udacity

Full Quadratic Residues Video Series: https://www.youtube.com/watch?v=EJv4TiYP8-s&list=PLsT0BEyocS2LmR8rtDQC-u_ueGHvzOwYi
Full Pell's Equations Video Series: https://www.youtube.com/watch?v=s5RQj_Jcs0U&list=PLsT0BEyocS2L25-tI-XUrWOJVvf4N3Ivq
In this video, I define what a Mersenne Prime is.

Views: 115
Polar Pi

Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/donateinfi
What is a the difference between a random and a pseudorandom number? And what can pseudo random numbers allow us to do that random numbers can't?
Tweet at us! @pbsinfinite
Facebook: facebook.com/pbsinfinite series
Email us! pbsinfiniteseries [at] gmail [dot] com
Previous Episode
How many Cops to catch a Robber? | Infinite Series
https://www.youtube.com/watch?v=fXvN-pF76-E
Computers need to have access to random numbers. They’re used to encrypt information, deal cards in your game of virtual solitaire, simulate unknown variables -- like in weather prediction and airplane scheduling, and so much more. But How can a computer possibly produce a random number?
Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow
Made by Kornhaber Brown (www.kornhaberbrown.com)
Special Thanks to Alex Townsend
Big thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!
And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!

Views: 128253
PBS Infinite Series

This talk will consist of a series of light mini-talks inspired by Atkin's papers on recognizing primes (1982, 'On a primality test of Solovay and Strassen'; 1995, 'Intelligent primality test offer'), proving primes to be prime (1993, 'Elliptic curves and primality proving'), factoring integers into primes (1993, 'Finding suitable curves for the elliptic curve method of factorization'), and enumerating primes (2004, 'Prime sieves using binary quadratic forms').

Views: 1708
Microsoft Research

The Prime Number Theorem is explained. The natural logarithm is introduced using the logarithmic spiral to give you a better feeling for this type of growth. These come together to give us an intuitive feeling AND formula for how many primes exist as we look towards infinity.

Views: 88853
Art of the Problem

Bairav teaching me Mersenne Primes, Perfect numbers and Pythagorean triplets.

Views: 266
Lakshmi Narayani

Matt Parker on the latest Mersenne Prime to take the title of "world's biggest prime". He had it printed!
More links & stuff in full description below ↓↓↓
More from this interview very soon, including details of how the prime was found.
PART TWO: https://youtu.be/lEvXcTYqtKU
PART THREE on Numberphile2: https://youtu.be/jNXAMBvYe-Y
Matt's interview with Curtis Cooper: https://youtu.be/q5ozBnrd5Zc
The previous record: https://youtu.be/QSEKzFGpCQs
Mersenne Numbers and Mersenne Primes: https://youtu.be/PLL0mo5rHhk
More on Mersenne Primes: https://youtu.be/T0xKHwQH-4I
GIMPS: http://www.mersenne.org
Prime Playlist: http://bit.ly/primevids
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
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Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile

Views: 745240
Numberphile

Introduces secondary students to the primes, making use of the sieve of Eratosthenes, and looks at twin primes, the spread of the primes, Euclid's proof of the infinity of the primes and Mersenne primes.
The worksheet can be downloaded from www.mathswithgeoboards.com

Views: 992
Maths with Geo-boards

This video gives an overview of primality tests. Basic ideas on how these tests work are discussed.

Views: 623
Leandro Junes

This is the first video of a new series, which will discuss a wide variety of famous (and perhaps not so famous) mathematical problems, ranging from antiquity to modern times. I am N J Wildberger, a pure mathematician at UNSW, the discoverer of Rational Trigonometry and Universal Geometry, and a big fan of YouTube, the future of free on-line education!
After introducing the series, we begin with FMP #1: how to factor a particular number z (10 to the 10 to the 10...altogether ten times, plus 23) into primes. We remind viewers about primes and the Fundamental theorem of Arithmetic, and have a look at explicit factorizations related to our basic problem.
Then we introduce briefly modular arithmetic and the theorems of Fermat and Euler. This is used to show that 7 does not divide z. Some comments on difficulties with arithmetic with big numbers follows, and then some exercises give some challenges for the viewer.
Thanks to Professor Saad El-Zanati from Illinois State University for suggesting this series. Thanks also to Steve Sexton from Exchange for giving permission to use their music track Highlights.
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.
A screenshot PDF which includes FamousMathProbs1 to 12 can be found at my WildEgg website here: http://www.wildegg.com/store/p111/product-FamousMathProblems-screenshot-pdf
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .

Views: 53285
Insights into Mathematics

Views: 93
Mike McCraith

There is a new "largest known prime number".
More links & stuff in full description below ↓↓↓
Extra footage: http://youtu.be/o0ZOs7sMS7k
More on Mersenne Primes: http://www.youtube.com/watch?v=PLL0mo5rHhk
Perfect Numbers: http://www.youtube.com/watch?v=ZfKTD5lvToE
Googolplex: http://www.youtube.com/watch?v=8GEebx72-qs
Graham's Number: http://www.youtube.com/watch?v=XTeJ64KD5cg
This video features Dr Tony Padilla from the University of Nottingham.
NUMBERPHILE
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Videos by Brady Haran
Patreon: http://www.patreon.com/numberphile
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Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile

Views: 489404
Numberphile

A History of Primes
Manindra Agrawal, American Academy of Arts and Sciences, October 2002
The Clay Mathematics Institute (CMI) 2002 Annual Meeting took place on Wednesday, October 30, 2002, from 2:30 to 5:30 PM, at the American Academy of Arts & Sciences in Cambridge, Massachusetts. The Annual Meeting brought together an international assembly of mathematicians to celebrate the universality of mathematical thought. This meeting provided a public forum for discussion among leading mathematicians and scientists, and it strengthened relations between mathematicians, the public, and the scientific research community.
The meeting began with the presentation of the 2002 Clay Research Award to Oded Schramm (for his work on the Loewner equation) and to Manindra Agrawal (for his work on primality testing). CMI President Arthur Jaffe and Directors Landon Clay and Lavinia Clay gave the awards. This Research Award recognizes major recent breakthroughs in two mathematical directions, and represents the pinnacle of recognition of research achievement by CMI. Each prizewinner becomes a Clay Research Scholar, and receives a bronze model of the CMI logo, an elegant sculpture "Figureight Knot Complement vii/ CMI" by sculptor Helaman Ferguson. Former winners are: Andrew Wiles, Laurent Lafforgue, Alain Connes, Stanislav Smirnov and Edward Witten.
Two talks followed the awards ceremony. Manindra Agrawal of the Indian Institute of Technology surprised all experts in August 2002 by solving an ancient problem (working with two undergraduate students). They showed that one could determine the primality of a number in polynomial time. This was the first talk in the United States by the inventor of the new method. Vladimir Voevodsky from the Institute of Advanced Study gave the second talk. He spoke about the mathematical breakthroughs that led to his receiving the Fields Medal in August 2002.
"We have a very impressive set of ground-breaking mathematicians at this year's meeting as award winners and speakers. The meeting certainly will inspire young mathematicians who attend, as well as all those who read about it or view the meeting on the web," said Arthur Jaffe, President of the Clay Mathematics Institute. "Agrawal will discuss his exciting discovery - the ASK algorithm for primality testing, and Voevodsky will explain his novel approach to the mathematical modeling of shapes known as "motivic homotopy theory."
http://www.claymath.org/annual_meeting/2002_Annual_Meeting/

Views: 13581
PoincareDuality

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 51644
nptelhrd

05 Aug 2014 - Bsides Las Vegas 2014
Joe "moloch" - Bishop Fox
Dan "AltF4" Petro - Bishop Fox
http://www.bishopfox.com
http://www.bishopfox.com/blog/2014/08/untwisting-mersenne-twister-killed-prng/
http://www.irongeek.com/i.php?page=videos/bsideslasvegas2014/bg04-untwisting-the-mersenne-twister-how-i-killed-the-prng-moloch
Untwisting The Mersenne Twister: How I killed the PRNG
Applications rely on generating random numbers to provide security, and fail catastrophically when these numbers turn out to be not so “random.” For penetration testers, however, the ability to exploit these systems has always been just out of reach. To solve this problem, we’ve created “untwister:” an attack tool for breaking insecure random number generators and recovering the initial seed.
We did all the hard math, so you don't have to! Random numbers are often used in security contexts for generating unique IDs, new passwords for resets, or cryptographic nonces. However, the built-in random number generators for most languages and frameworks are insecure, leaving applications open to a series of previously theoretical attacks. Lots of papers have been written on PRNG security, but there's still almost nothing practical you can use as a pentester to actually break live systems in the wild. This talk focuses on weaponizing what used to be theoretical into our tool: untwister. Let's finally put rand() to rest.
DISCLAIMER: This video is intended for pentesting training purposes only.

Views: 4582
Bishop Fox

This video shows you how to calculate the order of integers and how to find primitive roots.

Views: 20370
Cathy Frey

2012/01/10
My name is (John) Kooz. \I'm awesome. Join me for some Awesome Sexy Math
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SUBSCRIBE!!!! This Channel is a Good Vibe!!!!!!!!!!!!!
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http://www.validateyourlife.com MAIN Podcast and Blog of over 10 YEARS
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https://plus.google.com/u/3/photos/110142353241858683307/albums the late johnkooz who died on 2013/05/15

Views: 157
John Kuczmarski

Views: 5764
Eddie Woo

A two-minute news package I produced for Central News regarding UCM's Dr. Curtis Cooper's discovery of the longest known Mersenne prime number. At 22 million digits, this is Cooper's fourth prime number discovery.

Views: 582
Cliff Adams

I go through Euclid's classic proof of the infinitude of primes, in this, the third of Meep's Math Matters episodes.
If you have ideas or requests for math videos, please comment on the video or email me at [email protected]
And remember to spread the math love!
Reference: http://en.wikipedia.org/wiki/Prime_number#There_are_infinitely_many_prime_numbers

Views: 2966
meepsmathmatters

Two examples about the Miller-Rabin algorithm are explained in detail in this video.

Views: 554
Leandro Junes

Euclid identified Prime Numbers as building blocks for all numbers. This leads to the discovery of unique factorization. This idea lies at the heart of modern encryption techniques such as RSA.

Views: 18145
Art of the Problem

Prime Adventure: Learn how to build algorithms (and write code!) which solve number theoretic challenges such as prime factorization. Follow the rest of this adventure on Khan Academy: http://www.khanacademy.org/cs/prime-adventure-level-1/1018672065

Views: 33540
Art of the Problem

Number Theory: a^n-1 prime implies a=2 and n is prime (proof)

Views: 3264
DerivinDrunk

Math 706 Sections 6.3 and 6.4
Mersenne Primes, Fermat Primes and Sophie Germain Primes

Views: 371
Todd Cochrane

A perfect number is a number that equals the sum of its proper factors. How can we find them?

Views: 5342
shaunteaches

Paper: http://fermatslibrary.com/s/a-one-line-proof-of-the-infinitude-of-primes
Fermat's Library: http://fermatslibrary.com/
Follow Us on Twitter: https://twitter.com/fermatslibrary

Views: 19806
Fermat's Library

An introduction to an analytic proof of the theorem. More videos https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/videos

Views: 3730
Randell Heyman

Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 7707
nptelhrd

Presentation by Martin R. Albrecht, Jake Massimo, Kenneth G. Paterson, Juraj Somorovsky at Crypto 2018 Rump Session

Views: 140
TheIACR

Dr James Maynard, Fellow in Mathematics at Magdalen College, University of Oxford talks to Prof Denis Noble. They discuss the gaps between prime numbers, an area of study which won James the Ramanujan Prize in 2014. As well as the pure beauty of mathematical study, the work also has practical consequences - prime numbers are vital in cryptography and so therefore crucial in day to day activities such as protecting our credit card details when we shop online.

Views: 3547
voicesfromoxfordUK

© 2019 Wollongong university coal mining

FiNMAX, instead of trying out new concepts in binary trading, has taken all the accomplished products and services that are prevalent in the markets and added them to their brokerage account. As a result, what you get is a reasonably competent binary options account that cover all key aspects of binary options trading in an affordable package. Of course, not all is well with FiNMAX, as the broker has failed to address some of the pressing concerns that are relevant to its clients. In our FiNMAX binary options review, we give you a relatively transparent outline of what makes FiNMAX a good choice of a brokerage, and what are all the negative aspects that you should contemplate before opening an account. Under first impressions, it is clear that FiNMAX has clearly understood all the primary requirements of traders. In fact, FiNMAX tries hard to display itself as a genuine binary options trading company, despite its humble beginnings in 2016. It was certainly refreshing to see that FiNMAX is located in the UK, with additional offices in Bulgaria, Cyprus, Australia, Canada, and Italy. The professionally designed website also leaves no stones unturned as to the commitment of the company towards ensuring complete transparency in its products and services.