Over the past few months, I have been inundated with tweets about the largest prime number ever found. That number, according to Nature News, is . This is certainly a very large prime number and one would think that we would need a supercomputer to find a prime number larger than this one. In fact, Nature mentions that there are infinitely many prime numbers, but the powerful prime number theorem doesn’t tell us how to find them! Well, I am here to tell you of the discovery of the new largest prime number ever found, which I will call . Here it is:
This number, the product of all prime numbers known so far plus one, is so large that I can’t even write it down on this blog post. But it is certainly (proof left as an exercise…!) a prime number (see Problem 4 in The allure of elegance) and definitely larger than the one getting all the hype. Finally, I will be getting published in Nature!
In the meantime, if you are looking for a real challenge, calculate how many digits my prime number has in base 10. Whoever gets it right (within an order of magnitude), will be my co-author in the shortest Nature paper ever written.
Update 2: I read somewhere that in order to get attention to your blog posts, you should sprinkle them with grammatical errors and let the commenters do the rest for you. I wish I was mastermind-y enough to engineer this post in this fashion. Instead, I get the feeling that someone will run a primality test on just to prove me wrong. Well, what are you waiting for? In the meantime, another challenge: What is the smallest number (ballpark it using Prime Number Theorem) of primes we need to multiply together before adding one, in order to have a number with a larger prime factor than ?
Update: The number given above may not be prime itself, as pointed out quickly by Steve Flammia, Georg and Graeme Smith. But, it does contain within it the new largest prime number ever known, which may be the number itself. Now, if only we had a quantum computer to factor numbers quickly…Wait, wasn’t there a polynomial time primality test?
Note: The number mentioned is the largest known Mersenne prime. That Mersenne primes are crazy hard to find is an awesome problem in number theory.
As an undergraduate, I took Introduction to Algorithms from Ron Rivest. One of the topics he taught was the RSA public-key cryptosystem which he had created with Adi Shamir and Leonard Adleman. At the time, RSA was only about a decade old, yet already one of the banner creations of computer science. Today many of us rely on it routinely for the security of banking transactions. The internet would not be the same without it and its successors (such as elliptic curve cryptography, ECC). However, as you may have heard, quantum computation spells change for cryptography. Today I’ll tell a little of this story and talk about prospects for the future.
Ron Rivest
What is public-key cryptography (PKC)? The basic notion is due to Ralph Merkle in 1974 and (in a stronger form) to Whitfield Diffie and Martin Hellman in 1976. Their remarkable proposal was that two parties, “Alice” and “Bob”, could cooperate in cryptographic protocols, even if they had never met before. All prior cryptography, from the ancients up through and after the cryptographic adventures of WWII, had relied on the cooperating parties sharing in advance some “secret key” that gave them an edge over any eavesdropper “Eve”. Continue reading →
Arthur Wightman passed away this past January, at age 90. He was one of the great mathematical physicists of the past century.
Two of Arthur’s most renowned students, Arthur Jaffe and Barry Simon, wrote an affectionate obituary. I thought I would add some reminiscences of my own — Wightman was my undergraduate thesis advisor at Princeton.
I loved math in high school, and like many high school students before and since, I became convinced that Gödel’s incompleteness theorem is the coolest insight ever produced by the human mind. I resolved to devote my life to set theory and logic, and somehow I also became convinced that Princeton would be the best place in the world to study the subject. So there I went. I had a plan.
As a freshman, I talked my way into a graduate level course on Advanced Logic taught by Dana Scott. (I cleared the biggest obstacle by writing an essay to pass out of the freshman English requirement.) The course was wonderful, but by the end of it I was starting to accept what I had already sensed while in high school — I lack the talent to be a great mathematician.
A door was closing, but meanwhile another was opening. I was also taking a course on Electricity and Magnetism, based on the extraordinary book by Ed Purcell, taught by the charismatic Val Fitch. Chapter 5 contains an unforgettable argument explaining how electrostatic forces combined with special relativity imply magnetic forces. Meanwhile, while learning advanced calculus from the lovely (but challenging) little book by Michael Spivak, I realized that the Maxwell field is actually a two-form! Physics can be almost as cool as logic, so I would be a physics major! I had a new plan.
Of course they aren’t geeks! That was it…the whole purpose was to crack the image of the so-called “geek”. Having known that, since I was a Caltech alum turned filmmaker, I would get the stereotype and know the culture, Spiros came up to me 6 months ago and asked me if I could create a set of videos for outreach. These would be targeted towards getting high school kids more interested in science. Another facet of the videos would be to celebrate what we do here at Caltech and present it to be as “cool” as it really is. That began the talk of how many American kids these days stereotype science to be nerdy and “uncool”. With the recent advent of shows like Numb3rs and The Big Bang Theory, it is becoming more hip and popular to be a quintessential “nerd” or “geek”, but still a lot more work needs to be done to translate this effect into increasing the numbers of enrollment in science degrees. In a world where cultural slang is spoken more than language, we just can’t escape those titles of “nerd” or “geek”. Those terms often have negative connotations, but if we really look them up in a dictionary, this is what we get for “geek”: an enthusiast, or expert, especially in a technological field or activity. Now that isn’t so bad, is it?
So, we began with touring some of the labs of the agreeing advisors in the IQIM division, who were fine with a huge camera, a dolly track for movement and a couple of non-science strangers, namely our film crew, in their sensitive, experiment-running labs. I started meeting with the postdocs and grad students and not surprisingly, they inspired me. We realized that we wanted to celebrate the people behind the science and not the science, in this video. The science is known and celebrated in so many other avenues. It was about the scientists and how they did all these amazing things in addition to their scientific pursuits and oh, by the way, they did do some serious science too. To me, it was about making a more 3-D vision of the “nerdspace” out there in media for science and engineers. Breaking the identity that if you are a scientist, you are boring and all you do is work in the lab. What could have been the most risqué representation I thought… bingo: High Fashion! And then came the convincing…
Emma Wollman, with her drill and black gown.
We had a meeting where we asked people to wear tuxes and gowns and pick the one item that they would take with them if Earth was to be evacuated; the one hobby, the one piece of identity. Initially there was paranoia, nerves and resistance, but then I cut a pitch tape to give an idea of my theme and style. They were getting convinced, but still not too sold on being so high fashion. So we met halfway. It was not the initial black, formal event attire, but it was still clean cut whilst being real, and frankly, a lot more personal in the end. People came up with very interesting stuff, whether it was Emma Wollman who held a drill and wore a gorgeous draped black gown she made herself (!), or Chen-Lung Hung, who played a violin in the Kimble lab, or Erik Henriksen with his long, lightsaber-looking device, or John Preskill with his baseball glove!
John Preskill really likes baseball.
By putting them in the labs and their environments of science, but having a fashionable look, where they were lit especially to create distance from their environment thanks to the talented cinematography of Anthony C. Kuhnz, the shots became about the person more than the science in the labs, without completely separating them. It was their identity, but not all of it.
Another segment of the video that celebrates the power of “imagination and inspiration” is the inter-cutting of archival imagery of nature and science. Whether it is a ballerina’s spin bringing to life the spin of an atom, the probabilistic nature of the casino roulette metaphorizing the inherent indeterminism of nature, or water waves moving like a sine wave display in an oscilloscope, making the viewer aware that Physics is around us in ways that we might not even notice, is important. These juxtapositions with work that is being done here at Caltech may capture the eye of a new viewer who would initially react and say, “wait a minute…what does this have to do with science?” The video is supposed to be the hook, to intrigue and confuse and question and answer and I hope it does all this and, maybe, a little more.
A ballerina swiftly turns, hinting at quantum “spin”.
Of course, the punch to it all is the incredibly exciting and goose-bumping score by British composer, Andrew T. Mackay, part of the award-winning duo of Bombay Dub Orchestra, who, within a week, scored the video remotely from his Sunshine Desserts studio in London. Having worked with him on my feature film, we had developed a short-hand of what I like and it worked, within 9 days.
And all this crazy coordination and handling was thanks to Mrs. Marcia Brown who was always far too understanding and giving. She knows how to get us absent minded scientists and artists with our quirky moods and creative withdrawals, in line and on time to get the job done.
Lastly, I leave you with a few highlights of the video to urge you to click and watch and share. My favorite part of the video now, apart from Emma Wollman’s unbelievably attractive drill shot, is the beginning text that was a complete collaboration between me, Spiros and John Preskill with emails back and forth over a Wednesday in sunny Pasadena. Preskill’s genius tagline “nature is subtle” completely summarized my vision and the vision of IQIM and its scientists. The genius, the inspiration, the movement is all too important, yet subtle…and just purely “hot” in whatever sense of the word you want to take it!
Chen-Lung Hung with his violin. The text written in collaboration with John Preskill.
Here is the intro text in the video:
There is mind
There is matter
There is motion
There is interaction
There is the universe
To understand
To change
There is you…and your imagination.
IQIM
Nature is subtle.
And now, without further ado, I present to you, the IQIM Promotional Film. Sit back, relax, enjoy and share!
Editor’s Note:Pakistani filmmaker, Iram Parveen Bilal is the CEO and Founder of Parveen Shah Productions, a film production company with offices in Pakistan and Los Angeles. Having made and distributed a few short films, she is currently touring with her noted first feature length film, JOSH (English title: Against the Grain). Bilal is a Caltech alum, BS ’04 with honors, in Environmental Science Engineering and has an MFA from the USC School of Cinematic Arts in Filmmaking. Recent awards and fellowships include the 2012 Women In Film Award, the USC Stark Special Project Award, the Thomas J. Watson Fellowship, the Paul Studenski Fellowship, the Caltech Mabel Beckman Leadership Award and the Caltech Dean’s Cup.
As a mathematician, I often wonder if life would have been easier were I born 2,400 years ago. Back then, all you had to do to become eternally famous was to show that ( I am looking at you Πυθαγόρα!) OK, maybe I am not giving the Ancients enough credit. I mean, they didn’t have an iPhone back then, so they probably had to do by hand. All kidding aside, they did generalize the previous equality to other large numbers like (I am feeling a little sassy today, I guess.) Still, back then, mathematics did not start as an abstract subject about relations between numbers. It grew from a naive attempt to control elements of design that were essential to living, like building airplanes and plasma TVs. The Greeks didn’t succeed then and, if I am not mistaken, they still haven’t succeeded in making either airplanes, or plasma TVs. But, back then at least, my ancestors made some beautiful buildings. Like the Parthenon.
The temple of Athina (the Goddess of Wisdom, which gave her name to the city we now call Athens after a fierce contest with Poseidon – imagine flying into Poseidonia every time you visited Greece had she lost) was designed to be seen from far away and inspire awe in those who wished to conquer the city-state of Athens. But, those who were granted access to the space behind the doric columns, came face to face with the second divine woman to ever make Zeus stand in attention, whenever she met her dad on legendary Mt. Olympus: Αθηνά. And so, Φειδίας (Phidias), that most famous of ancient Greek sculptors, decided to immortalize Athina’s power with a magnificent statue, a tribute to the effortless grace with which she personified the wisdom of an ancient culture in harmony with the earth’s most precious gift – feta cheese.
Here she is, playing an invisible electric cello next to Yo-Yo Ma (also invisible). And yes, she liked to work out.
OK, I may be biased on this one. For Greeks, virgin olive oil and φέτα cheese go like peanut butter and jelly (I didn’t even know the last two went so well together, until I left Greece for the country of America!) Oh yeah, you are probably wondering what feta cheese and olive oil have to do with the Goddess of Wisdom. Well, how do you think she won over the Athenians, against Zeus’ almighty brother, Poseidon? The olive branch, of course. The sea is good and all (actually, the sea is pretty freakin’ amazing in Greece), but you can’t eat it with feta – you can preserve feta in brine (salt water), which is why Poseidon had a fighting chance in the first place – but, yeah, not good enough. Which brings us to the greatest rival, nay – nemesis, of the first letter with an identity crisis, : The letter . You are most likely familiar with the letter-number (you may have even seen the modern classic, American Pie, a tour-de-force, honest look at the life of Pi. No pun intended.) But, what about the number ? Well, I could tell you all about this number, , named after the sculptor dude above, but I ‘d rather you figure out its history on your own through this simple math problem:
The divine proportion: Does there exist a function , such that , and for all ?
Well, I am here to tell you of the discovery of the new largest prime number ever found, which I will call 
( I am looking at you Πυθαγόρα!) OK, maybe I am not giving the Ancients enough credit. I mean, they didn’t have an iPhone back then, so they probably had to do 
by hand. All kidding aside, they did generalize the previous equality to other large numbers like 
(I am feeling a little sassy today, I guess.) Still, back then, mathematics did not start as an abstract subject about relations between numbers. It grew from a naive attempt to control elements of design that were essential to living, like building airplanes and plasma TVs. The Greeks didn’t succeed then and, if I am not mistaken, they still haven’t succeeded in making either airplanes, or plasma TVs. But, back then at least, my ancestors made some beautiful buildings. Like the 
: The letter 
. You are most likely familiar with the letter-number 
(you may have even seen the modern classic, American Pie, a tour-de-force, honest look at the life of Pi. No pun intended.) But, what about the number 
? Well, I could tell you all about this number, 
, such that 
, 
and 
for all 
?
Quantum Frontiers 