# The Trinity Hall Prime – Numberphile

This picture, seen from far away, looks like a shape. And this is the coat of arms, or the Emblem, of Trinity Hall, this College, which is founded in 1350. 1350, by the way, is a significant date because it’s the year after 1349, and 1349 is the year of The Great Plague in London, one of the great plagues, and that wiped out the entire and laywer generation in London. And some people thought It was an act of God, but the founder of this college, Bishop Bateman, saw that the new generation of lawyers had to be retrained, and that’s why the 5 colleges were founded in the first place, but anyway, we don’t have to have that in recording- ____________ So we have a very strange object. This is the coat of arms of Trinity Hall. If you look closely it consists of eights and ones. Ohhhhhhh. (My God) There is a little bit of irregularity here but otherwise it’s followed by zero zero zero zero and, ends in a one. This turns out to be a prime and the number of digits in prime is 1350, which is the year of the foundation of the college. This was a gift from JF Mckee whom I didn’t know personally, but my senior colleague Tom Khanna did. He was a junior research fellow and was a postdoc of this college, who came maybe 20 years ago,

I am told by Tom and then when a fellow of the college leaves the college, it is traditional for that fellow to leave some gift to the College, and usually it has to do the subject. And he, rather enterprisingly, left this gift to the College. The coat of arms of Trinity House with lots and lots of zeros at the end, but with one and which is a prime. Now, how surprising is that? I’m really lost in awe of somebody who not only had this idea, but actually implemented this idea, and I think even today, It’s a bit difficult to check that this number is a prime I mean there are lots of Prime’s in the world of special types. For example, Mersenne primes and what-have-you. And for which, the y’know, algorithm for checking that they are prime, checking and primality is a very well-known piece of mathematics But this is a, fairly, sort of random prime. I mean it starts with eight, eight, eight, eight and then so on, and so, How do you discover such a thing is prime? And the purpose of his game of course was to hit the prime exactly at 1350. This is because it’s the year of the foundation of college So, you can’t really fine tune and with a number of digits. That’s why I think there’s an irregularity here in the beginning- zero followed by six, two, one. And, we are still looking for the special significance Of the number six to one. I’m sure there is some cosmic importance to this number as well. Brady: What’s your attachment to it? Tadashi: To be honest it’s sitting in the lunchroom, but I think most fellows don’t notice its presence. It’s just sitting there among some dictionaries and books on the side of the, erm, of the table and every once in a while when somebody like you, who has interest in science and who has a mischievous aspect to the personality, visit the college I love to show this to the people and they’re all kind of amazed. Again, not that somebody had an idea, but somebody actually implemented this whole thing is it’s really honorable(?) I think. Brady: Since recording with Tadashi, we’ve shed a bit more light on the identity of the mysterious prime number creator, JF McKee. It is in fact James McKee. Here he is around the time he was a research fellow in Pure Mathematics at Trinity Hall and here he is now where he’s a full professor at Royal Holloway. I did chat with him on the phone and by email, and if you’d like to find out more, have a look in the video description. *Tap, Tap* Tadashi: And the point farthest from the handle *Tap, Tap, Tap* *Tap* *Tap* Behave exactly the same way whereas 45 degrees off *Tap, Tap, Tap* *Higher Tap, Tap, Tap* *Tap, Tap, Tap* *Higher Tap, Tap, Tap* You get the hi-

621 is probably meaningless and just the result of making the image work with the given constraints, including having as many 0s as possible at the end.

Surprised to hear Bach at the start, Invention no. 1 if Im right?

You should make an interview with the creator to explain a little more than the explanation on the description.

How this idea was born. Etc.

Am I crazy, or are there only 1290 digits there?

I honestly think this guy has my favourite voice and accent ever.

;0; i dont get this Im in 6th grade

;-;

There is a video about gaps between primes and, if I remember well, the gaps are not that large. So I think the work to make a picture out of numbers like the on on the video really comes down in first arranging all the numbers like a picture without giving much a thought if it's affecting the final prime result and only starting to worry when you get to the last digit. Then you will have to start testing if the number is prime or not and, if it's not prime, just go to the next odd number (skipping 5). I don't know if a 1350 digit number nowadays is hard or not to test if it's prime..

Are there any other prime numbers that could qualify as a Trinity Hall prime?

Hey Numberphile, I was wondering if somebody could make a video about the maths and probabilities of the game show Deal or No Deal. I think that would make for a very interesting video. Love this channel by the way!

BACH INVENTION 1

My theory is that he simply created the 30×30 image with 8s and 1s followed by 15 rows of 30 0s, and tacked a 1 on the end to make it odd. From there he just methodically changed numbers at the beginning of the set of 0s and tested it until he found a prime number. If the 0621 is of any significance, then I expect he moved its position among the 0s around until he found a prime. It's even possible that the number of rows of 0s is also arbitrary, and he simply increased it whenever he had exhausted his options within the existing field of 0s. I've not studied prime numbers, but this seems like a very plausible way to create the image. As long as you have a sufficiently large area of the image that can be modified without ruining the effect, you can search a huge space of numbers and probably find a prime number in there somewhere.

Crítica social deix

Prof Tokieda is my hero, always and forever.

Sounds like the number is not prime. Practical Joke.

E621 is monosodium glutamate, which is responsible for one of the five basic tastes, umami.

I thought this was Numberphile, not show and tell. This video feels like it has no content, no depth. What did I walk away with learning from this? There's some random ASCII art prime. That's it. Nothing about how it was found, or anything meaningful. I would have liked to see something else done with this idea. What a waste.

Has anyone actually checked that the number printed is prime? I would love to find out that the whole thing was a prank. …And given that the description gives further insight, I must assume that the plot thickens! Most likely, the three non-zero digits were thrown in so as to provide this "plausible explanation" that would dissuade future mathematicians from discovering the prime factorization of this number!!

This is also prime. The 621 is replaced by 4 symmetric 1's on each side:

888888888888888888888888888888

888888888888888888888888888888

888888888888888888888888888888

888111111111111111111111111888

888111111111111111111111111888

888111111811111111118111111888

888111118811111111118811111888

888111188811111111118881111888

888111188811111111118881111888

888111888811111111118888111888

888111888881111111188888111888

888111888888111111888888111888

888111888888888888888888111888

888111888888888888888888111888

888111888888888888888888111888

888811188888888888888881118888

188811188888888888888881118881

188881118888888888888811188881

118888111888888888888111888811

111888811118888888811118888111

111188881111111111111188881111

111118888111111111111888811111

111111888811111111118888111111

111111188881111111188881111111

111111118888811118888811111111

111111111888881188888111111111

111111111118888888811111111111

111111111111888888111111111111

111111111111118811111111111111

111111111111111111111111111111

000000000000000000000000000000

000000000000000000000000000000

000000000000000000000000000000

000000000000000000000000000000

100000000000000000000000000001

000000000000000000000000000000

100000000000000000000000000001

000000000000000000000000000000

100000000000000000000000000001

000000000000000000000000000000

100000000000000000000000000001

000000000000000000000000000000

000000000000000000000000000000

000000000000000000000000000000

000000000000000000000000000001

Having a CS background, this wouldn't be all that hard; once you've got the first half, you randomly generate "irregularities" to fill in the second and test them. Since you've got about a one-in-3000 chance of hitting a prime (and that's before applying common sense constraints like not letting the last digit be even or 5), and randomized algorithms can test fairly quickly, you're bound to find an appropriate one before too too long.

Where's that link!?

When JF McKee created this, he was in his prime.

If the number is only ones. Is it a prime?

1, 11, 111, 1111?

Love Tadashi

2:36 Trinity and Trinity Hall are different colleges

Okay I didn't get a word of what he's saying

"We don't have to have that in the recording."

puts it in the recordingOne possible explanation about the 0621:

F is the 6th letter of the alphabet.

U is the 21th leter of the alphabet.

So maybe, just maybe, McKee was really happy about leaving?

It's divisible by 73. Not a prime.

621 is a Harshad number.

621/(6+2+1) = 69

seems like it was an hidden joke.

If you add an "i" at the end of tadashi's name it means "correct" in japanese… thought it was pretty cool…

If I make a website to generate this kind of a thing for you, how much would you pay? $5?

What if the number doesn't read left to right, but up and down. Or alternating lines of left to right, right to left or up and down then down and up. Do these variances come out as primes? The up-down method removes the 621 and the alternating left-right, right-left creates a 126 instead of 621. How about reading it as spiraling inward clockwise or counter clockwise?

That court at the start looks more like Trinity College's Great Court haha

Does anyone know more details on how numbers of this form can be checked for primality? It looks like the Generalized Pocklington method could work ( https://en.wikipedia.org/wiki/Pocklington_primality_test#Generalized_Pocklington_method )

Factor N-1 as N-1 = A*B, where A = 10^m. If A > sqrt(N) and relatively prime to B (meaning the shield pattern cannot be even or end in 5), then the generalized Pocklington test can be applied. Does that seem like the right approach?

Did the angle of the painting on the left annoy anyone else?

my name JF

I could listen to this gentleman speak all day! What a pleasant individual!

can someone explain, why his "Why do YouTube views freeze at 301?" Video has 301 views? ^^ he wrote in his video discription "This glitch was finally "fixed" in August 2015, but may it live on in our hearts.". Did something like a YouTube Admin that or are still all Videos back in the days with that glitch at 301 Views?

Kind of a useless video to be honest… explain about primes of these form and how it might have been derived! How long does it take to check that it's prime? If it takes so long how was the prime found in the first place?

well 6+2+1=9 same as 1+3+5 same as 1+8. now what is the significance of 9 in all that

where's the follow-up video!?!!?!?!!?

I love Tadashi. I could listen to his musings for hours and hours.

Edit: Aw…. as soon as I get settled in, the video's done. Bummer! Neat prime, though! Time to watch Tadashi reruns

I think what I like most about this video the most is that it implies that, given kilodigit integer, there is a high probability you can change it into a prime by altering only ~3 digits. In fact, this holds up nicely, since (assuming McKee simply permuted the first 4 digits of the 06210000… sequence) that in turn implies that the density of kilodigit primes is between 10^-4 and 10^-3, and the prime density approximation function (1/log(n)) gives a density of 4.3*10^-3 (or 3.2*10^-3 for 1350 digits)

Most awesome ASCII art ever.

I actually had to watch with closed captions. Sorry Tadashi.

Try doing the game snake in higher dimensions

It's a prime, prime created by a prime, prime creator.

An unproven conjecture can be stated as follows: "There is no prime number that ends in 8." This is today considered one of the three most difficult challenges in all mathematics. Compounding the difficulty, of course, is that mathematics currently lacks the methodology to prove a negative. Using the best computers of the day, mathematicians have ruled out that such a number exists anywhere between 2 and 1,000,000. But beyond that is fair game for some enterprising young mathematician looking to make a name for him/herself.

Only bankers are interested in sub-prime….

621 equals to 404 plus 217, two error codes.

I would love to see your take on the Wheel theory number system. I don't understand it fully, it's quite technical, but there are no videos about the topic here on YouTube and I think it's pretty interesting, being able to divide by zero and stuff like that. So, this is a big opportunity for an epic video, if you've got someone who can explain it relatively easily 🙂

thanks for bach

If you liked this, then take a look at Tupper's Self Referential Formula. It's a blast!

I think you could use the Pocklington–Lehmer primality test to do this (if anyone cares…)

621 is my locker combo lol

Did anyone else notice Bach's Invention in C major at 0:00?

Could you do a video on Carlyle circles? I find them very interesting and I would like to learn more about them from you.

If you are looking for a channel that explains, learns and talks about everything, congratulations for you in the perfect channel .. Subscribe to the channel and wait for exclusive videos in the near future.

zeta ( 2n ) = ( – 1 )^( n – 1 ) B_(2n ) * pi^(2n ) * 2^(2n – 1 ) / (2n )!

A

A

AA

AAA

AAAA

AAAAA

AAAAAA

Tadashi's toys? I thought Tadashi's toy is Baymax.

If the 621 doesn't have any special significance you can do with replacing just one zero by another digit: …000 900 001

March 16, 2017. I was reading my favourite book One, Two, Three, Infinity in the imaginary numbers section. It explained that people could only think of two numbers that added to 10 (I will call this x) and multiplied to 40 (I will call this y). Those two numbers were (5 + √-15) and (5 – √-15). The FOIL formula can show how this works. I looked at these two numbers and tried to find the formula that would work for other numbers (e.g. x = 2, y = 10). The formula I came up with was that the first number would be (x/2 – √-(y-(x/2)^2)) and the second number would be (x/2 + √-(y-(x/2)^2)). I was 15, then. I am guessing this formula already exists, but I haven't found it yet.

First start with a cylinder with the radius larger than the height of the cylinder. Then start to shrink the radius. The volume of a napkin ring around the cylinder will always be the same, and the volume of one of the other two caps goes from larger than the napkin ring to smaller than it. Therefore, there is somewhere between where the volumes are equal.

How do you even discover that

super derpy !

What's the link for more info with JF McKee?

In case you were wondering, the music at the beginning is "Invention No. 1" by Johann Sebastian Bach.

Does anybody else think Tadashi has an extremely soothing voice?

Link is not in the description

"Has a mischievous aspect to their personality" should be an accolade dispensed by Cambridge.

Let's be honest, half of the views here are from furries

So, by the description, I'm guessing there was simply a high chance of there being at least one prime fitting the desired criteria at that length, and it was just a matter of looping over some of the digits until one showed up. Interesting!

Why noone is talking about the row and coloumn width to make this possible

Tadashi is a legend

It is so weird that he came up with that. I wonder how.

Fancy bonkers.

Can we have a video to explain the explanation in the description?

I had Professor McKee as a lecturer at Royal Holloway for (unsurprisingly perhaps) Computational Number Theory. I don't know if he made this line up but this was in his lecture notes on primality testing: "even numbers are rarely prime, and even primes are easy to spot, so from now one we will assume that p is an odd prime!"

breathe inT R I N I T Y L O LIs it possible that it was 621 years from 1350 when he donated it?

Does Tadashi teach at Trinity College?

Anyone know the music(Bach's well-tempered Clavier) at the beginning?

Amazed. Yes. That would be it.

1444 is the best year tho

That's just about the greatest gift I've ever seen anyone give away.

WHAT THE FUDGING FUDGE?!?!?!

I think 621 means 6 & 21 and are representative of letters of the alphabet. James McKee was letting the college know what he really thought.

The anarchisms of 0.31 are painful

Yay Bach.

owo

0:41 "But anyway, we don't have to have that in the recording"

Puts it in the recording621:

existsFurries: OwO

furries are coming, prepare yourself

that guy just wanted to hint that he likes e621, thats all

This thing sits in the lunchroom?! This is such a cool gift to leave to a college! It should hold a place of honour!

Yeah you can check primality for a number like this using the Pollard p-1 algorithm. Basically, if p-1 consists of only small prime factors, then it's easy to show p is prime (and in fact, factor p if it is composite)

E621 is safe and nsfw too

E926 is safe only

Ok?