5, 13 and 137 are Pythagorean Primes - Numberphile

[@numberphile]

indeed.. glad you liked it!

[@mint-sh7yu]

Sure did

[@Murat-ji9ut]

Yeah

[@MrSiwat]

I'm a big fan of Prof. Eaves maths/physics chats. 1/137 was a classic but my favourite is the Planks constant and Dirac's large number hypothesis vid. plus extra footage. It's great to see him back in action again.))

[@aesdeef]

Before I saw the video I thought you'll be talking about Pythagorean triples where the lenght of the hypotenuse happens to be a prime number. It actually works for all the three numbers mentioned in the title: (3, 4, 5), (5, 12, 13), (88, 105, 137) ;)

[@abstractapproach634]

I wonder the probability that a prime holds both characteristics (a "pythagorean prime and a prime hypotenuse if a pythagorean triple) p = n² + m² /\ p² = j²+ k² :p is prime and n,m,j,k are integers p² = n⁴ + 2n²m² + m⁴ = j² + k² 2 equations, 5 unknowns so it's a 3D subset in 5D space (that's not proper language, but a 5D subset with is equal to its projection onto a eD space us wordy) Huh interesting

[@mennoverhoeven8735]

That's not a coincidence: it will always work :-) Suppose p is a Pythagorean prime, and m^2 + n^2 = p, then you can construct the following Pythagorean triple: (m^2 - n^2)^2 + (2mn)^2 = p^2

[@numberphile]

cool, glad you like them... hope you're checking some of the other channels!?

[@numberphile]

I've posted Professor Eaves' old sixtysymbols video on 137 (the fine structure constant) as a video response and it the video description!

[@shahrizavan5209]

Hi

[@shahrizavan5209]

137

[@numberphile]

a quick way to find them all is my website - bradyharan com

[@GretgorPooper]

When professor Eaves says "pythagorean prime", it kinda sounds like the name of some powerful magical creature, because of his voice.

[@AlexLococo]

Behold my creation! Pythagorean Prime!

[@jennywilliams7231]

Some new uber badass transformer

[@felipelopes3171]

But that's exactly what it is!

[@carlrodalegrado4104]

It's Optimus Prime long lost brother who was suppose to be the next prime

[@pauliedweasel]

It’s the cultured tone of the the king’s English being spoken by a highly educated subject of the realm.

[@fromMouq]

2 is the prime constructed by 1^2 + 1^2 unless I'm missing something. I refer to the list @ 3:11 It was just something I noticed; It's a wonderful video

[@georgemissailidis7581]

I love how all of a sudden at 1:11 he pulls out a right-angle triangle out of nowhere

[@georgemissailidis7581]

Also, how many pythagorean primes are Fermat primes? If a pyth. prime is 4n + 1 and a Fermat prime is 2^n + 1 then 2^n = 4n so the only solution is if n = 4 which shows that 2^4 = 4^2 which is true. Something special about 17 !!!

[@aletoledo1]

This is starting to become one of my favorite channels.

[@OrlinNorris]

137 is my favourite number!

[@ryansteele2446]

OrlinNorris 137 is the 33rd prime

[@Very.Crazy.Math.Pistols]

Also mine 😉

[@hellstormangel]

Same

[@iordanneDiogeneslucas]

@1729 math_blog the fractal universe

[@VindexAnimae]

Wolfgang Pauli who is obsessed with alpha 1/137, he died in room 137. 🔺

[@numberphile]

done that one already!

[@D13djeej]

HAPPY BIRTHDAY, MATE

[@RoaringTRex]

You think of great questions to ask, Brady!

[@NoriMori1992]

I love this guy's accent and voice.

[@AussieEvonne]

Really nice to see Prof Eaves again!

[@daninewman9544]

My daughters birthday 17th May so my favourite is 175 including Matrix . 71, 157 half of Pi, 571 and 751. Cheers. All Primes

[@michaelempeigne3519]

one can develop these numbers by the fibonacci sequence. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ......................... if we take four consecutive fibonacci numbers say : 1, 2, 3, 5 multiply the two outer numbers ( 1 * 5 = 5 ) double the product of the two inner numbers ( 2 * 2 * 3 = 12 ) and can figure out the third number by 5^2 + 12^2 = 13^2 this can be done for any fibonacci numbers. Furthermore we can find the area of the triangle generated by multiplying all four fibonacci numbers together : 1 * 2 * 3 * 5 = 30 and the perimeter is double the product of the last two fibonacci numbers : 2 * 3 * 5 = 30

[@travisbaskerfield]

Never knew that. Lovely! Don't know what you think of numerology, but "The Mystery of Numbers" gives the number 2701 (using the model of Hebrew gematria on the 26 (= YudHeVavHe) letters of the English alphabet). 2701 is the Hebrew gematria of the first verse in Torah. 2701 = 37*73, mirrow primes with mirror indices. "The Numbers Three and Seven're considered Perfect in Qabala" also gives 2701.

[@tompurcell1499]

+travisbaskerfield Numerology is not my thing but here's a little fun fact: 37 is number 12 on the list of primes while 73 is number 21. Do I hear Twilight Zone music in the background?

[@joulesjams20]

Michael Empeigne nice property this can be seen from the identity (m2-n2)2+(2mn)2=(m2 +n2) 2 where m2 is m squared and m and n are coprime. Also this works with any sequence formed by adding the two previous terms so it's not unique to the fibonacci numbers.

[@stygn]

Finally one on numberphile who writes the "7" correctly. It's supposed to be stroked. (And I could tell you why...)

[@devinbrown6272]

Tell me

[@fiiredark]

Because in the original version of how to write the set of symbols we still use to express numbers today, each symbol contained the same number of angles within itself as the number the symbol was trying to express. (Just the single digits 0-9 of course.) 0 has zero angles. 1 as it typically appears in type has one angle. 2 is written like a ‘z’, and thus contains 2 angles. Make the curves of 3 into points instead. Three angles. Look it up. Some numbers are slightly trickier to explain in words, but they are completely recognizable when you see a picture. You’re welcome ;)

[@W4LL37SK83R]

when i first saw this video, i assumed they were called Pythagorean primes because they were part of Pythagorean triples (3,4,5; 5,12,13; 88,105,137; etc.). its weird how it works for the same numbers (17 as well)

[@MrDbm101]

what are the other channels besides sixty symbols...i'm addicted to these videos.

[@Nao_Miria]

I too love the number 137, it has been my favourite for a long time, just randomly (kind of). Over time I keep finding out cool things about it :D

[@ffggddss]

Fun stuff! My only disappointment was failure to point out that, while for each Pyth. prime, p, √p is the hypotenuse of a rt. triangle with integer legs (a, b), so is p itself! (with bigger legs, of course) And you can get the legs for the bigger triangle, by squaring the corresponding complex integer with the smaller legs: (a + bi)² = a²-b² + 2abi So for p = 137 = 11² + 4², you have 11² - 4² = 105; 2·11·4 = 88, so: 137² = 105² + 88²

[@ffggddss]

The point is that when you plot these in the complex plane, the length is the Pythagorean sum of the x (real) and y (imaginary) components: z = x + iy ; |z| = √(x² + y²) All this really says is that if you draw the corresponding right triangle, with a along x, and b along y, then c, the hypotenuse satisfies the familiar Pythagorean Theorem: a² + b² = c² Now when you square a complex number, its length also gets squared. Which means that the squares of the new components (A=a²-b² and B=2ab), also satisfy the Pythagorean Theorem, with: A² + B² = C² = (c²)² (a²-b²)² + (2ab)² = (a² + b²)² So in my example, a=11, b=4, c=√137, c²=137 A = a²-b² = 105 , B = 2ab = 88 , C = c² = 137 C² = 137² = 105² + 88²

[@ffggddss]

Yes, it's one of those totally marvelous techniques that makes me wish I'd thought of it!

[@ISmokePopRocks]

5.13 is also my brothers birthday and 513 is one of those numbers I see everywhere, this video is just another

[@russellthorburn9297]

I was wondering whether the connection between 137 and the fine structure constant would be mentioned.

[@JonathanTot]

ya, this is what i meant prefix this with the definition that a pythagorean prime (PP) is a prime of form 4n+1 this is equivalent to saying the definition that PP is the sum of two squares and prime and that is equivalent to the definition that a PP is a prime hypotenuse of a pythagorean triple

[@l37baconstrips]

I love the # 137 because a used to go on route 137 on vacation. This was when i was a little kid. Now seeing this math is really cool!

[@sillymesilly]

137 is an inverse of a fine structure constant

[@numberphile]

yeah it was my very clumsy question that caused the problem... but I think you know what was meant!

[@NowhereManForever]

Someone else who loves 137

[@mclainv]

137 is seriously my favorite number.

[@Minecraftster148790]

I love it. Did u know what the mass number of barium is? U will never guess. It is 137

[@screes620]

137 is the number of degrees turned when using the golden ratio for dropping seeds around a plant.

[@chrisg3030]

137, 173, 317 are all primes. The next three permutations in ascending order, 371, 713, 731, and the mirrors of the previous, are composites. Unique?

[@MrRikimari]

Does 1307 count as 137? My apartment unit is 1307 😃

[@JonathanTot]

in fact they are equivalent. if p is one of these pythagorean primes as described above, then p=a^2+b^2, which can be factored into a product of complex conjugates p=(a+ib)(a-ib) then p^2=(a+ib)^2*(a-ib)^2=(a^2-b^2+2abi)(a^2-b^2-2abi) this again is a product of complex conjugates, so p^2=(a^2-b^2)^2 + (2ab)^2

[@FrogDaBomb]

Note: if m^2+n^2 = c, for integers m and n, then there exists integers a and b such that a^2+b^2 = c^2. (By Euclid's Formula). I'm surprised that wasn't in there....

[@wolken_bruch]

My birthday is the 13th may too :D It's kind of satisfying.

[@edwardevans2577]

+BibiCookiecat Same!

[@numberphile]

hi, my other channels include sixtysymbols, periodicvideos, nottinghamscience, deepskyvideos, foodskey, backstagescience, etc...

[@NickiShinn]

The example he gave us, which was A = 3.2 inches and B = 5.75 inches, then C is about 6.5804635095105572661826405151142 inches.

[@Alex-rk3gv]

The month I was born on was the 6th and the 28th day. its a perfect number day, and its the only one in a year!

[@walterrobinson9796]

What about 6/6?

[@atticuswalker]

has anyone noticed that the fine structural constant is almost the same as the half the decimal in pi. that 137 has a repeating decimal of 8. and mass as a wave repeats after 8 turns.

[@timlavy1968]

It just so happens that 5 and 13 are also the hypotenuses of right-angled triangles when the legs are integers. Because sqrt(3^2+4^2)=5 and sqrt(5^2+12^2).

[@jimharmon9917]

It is the SQUARE of the hypotenuse of an integer right triangle that might be a Pythagorean prime - not the square root of the hypotenuse.

[@JAlexCarney]

Jim Harmon but a square number can never be prime : p so that is a really silly definition

[@jimharmon9917]

I will parenthesize my statement to make it more obvious what I meant: It is the SQUARE of (the hypotenuse of an integer right triangle that might be a Pythagorean prime). That is, the value of the hypotenuse being the prime, not its square.

[@ffggddss]

Some salient facts, not all of which are brought out in the video: 1. Every prime is either 2, or is congruent to either ±1 (mod 4). 2. Every prime that is 2 or == +1 (mod 4), and no other prime, is expressible as a sum of two squares. 3. Every number, n, that is expressible as a sum of two squares, and whose sqrt, √n, can thus be the hypotenuse of a right triangle with integer legs (a,b, so that a²+b²=n), can also itself be the hypotenuse of an integer right triangle, by virtue of squaring the complex integer a+bi, and using the squared length of that complex integer: (a+bi)² = a²-b² + 2abi ; (a²-b²)² + (2ab)² = (a²+b²)² = n²

[@somosUS]

The value of the length of the hypotenuse squared which would be the Pythagorean prime. In His example, for instance, a right triangle with sides a=11 and b=4 would have a hypotenuse of length 137^(1/2). We can show this by applying the Pythagorean Theorem: a^2 + b^2 = c^2, for a=11 and b=4 would be (11^2)+(4^2) = c^2 = 137 (the prime number.) To get the length of the hypotenuse, we would need to take the square root of our Pythagorean prime, which would be roughly 11.7047.

[@koenth2359]

Parker square of the hypothenuse

[@TazManiac008]

I LOVE your videos and I have watched them all, but the sound of the markers on the paper makes me shiver to the bone!! Please use a white board, you'll make me one happy viewer.

[@Astromath]

I'm glad they didn't listen to you xD

[@IceMetalPunk]

Prime numbers (especially large ones) are important in cryptography. Pythagorean primes can be generated by the constraints a^2+b^c=c and 4n+1=c; having a nice way to generate prime numbers, even a subset of them, is useful.

[@GyanPratapSingh]

I think this is the first time anyone has ever messed up on one of those brown sheets of papers that are in Brady's videos

[@Talpykaze]

cuz the diagonal can be calculated as a^2+b^2=c^2 and then take the square rot of c^2 and u get the diagonal. and he used the same method to get 5, 1^2+2^2=c^2, c^2=5

[@theGraphicAutist]

So THATS why our Rick and Morty reside in universe c137! They said it was arbitrary!

[@nnmdani]

Happy Birthday :)

[@AtheistCitizen]

k >0 forces the lengths A,B,C of the corresponding rt triangle to be positive. If you want to "play" with sign and do not associate PT with a triangle then +/- any A,B, or C but this will not add new Natural number solutions, hence no new triangles. PP with a=b solution is unique at PP=2. Other a=b solutions? Wd imply prime divisible by 2 [so no others]. Silly case to consider. So a or b, one must be larger. WLOG let a>b keeps all A,B,C positive so the solution corresponds to a right triangle.

[@PhilBagels]

I wonder how many Pythagorean primes are also hypotenuse lengths for Pythagorean triples. Both 5 and 13 are. 5 = 2^2 + 1^2, but also 5^2 = 4^2 + 3^2. And 13 = 3^2 + 2^2, but also 13^2 = 12^2 + 5^2. And 17^2 = 15^2 + 8^2. And 29 = 5^2 + 2^2, but also 29^2 = 20^2 + 21^2. etc. And... wait for it... 137^2 = 105^2 + 88^2

[@SmileyMPV]

but 2=1^2+1^2 and 2 is prime, while there exist no 2 natural numbers a and b such that 2^2=a^2+b^2 :(

[@Deathranger999]

All of them are, in fact! It's a known fact that all Pythagorean triples take the form (2kmn, k(m^2 - n^2), k(m^2 + n^2)), with k, m, and n integers with either m or n even, and m > n. I could prove that, but the margins of this comment are too small (in all serious, it's not that hard of a proof). So all Pythagorean triples look like that. In all of them, k(m^2 + n^2) will be the hypotenuse. So you can see that if k = 1, then the hypotenuse can always be represented as m^2 + n^2 for integers m and n. So if m^2 + n^2 is a prime, then it's also the hypotenuse of some right triangle. :)

[@Deathranger999]

+Kieran Kaempen also, m != n.

[@VWftw82]

I like 233 because the roots of the perfect squares which add up to it (8, 13) are the parts of the wedding anniversary of a cousin of mine.

[@coc235]

And also all these three numbers are in the Fibonacci sequence!

[@MarcusArmstrong037]

My youtube account used to have the number 137 in it, because I thought it was an awesome number. Now I have another reason to like it.

[@nerd9347.]

Neat. Happy birthday!

[@Ofordgabings]

137 is one of my favorite numbers because it's Porygon's number, which is my favorite pokemon. Okay now I feel really nerdy... =/

[@AndrewBarth]

@numberphile You should do a video on the Dyson Number!

[@NielsBlok567]

137, of course!

[@Enigma1790]

Pythagorean primes are special because they fit both the pattern of Pythagorean numbers and primes. That's it. Mathematicians love this kind of thing. I mean they make such a deal over Mersen primes and prime numbers in general for example. It's really quite arbitrary. Not to say I don't love mathematics, because I do, and it is cool to find patterns or particularly rare occurrences, but a lot of it seems arbitrary if you lack higher understanding like I, or most people do.

[@numberphile]

oh I forgot to do that trick! :)

[@mageknight6166]

What about two? Two is prime. 1²+1²=2 Is it not also Pythagorean, despite not following the 4n+1 property?

[@joaolucasgaldino9872]

The thing is, they don't count as prime.

[@bradsa82]

John Galdino 2 is prime. Just the weird one that doesn't follow the others. 1 however isn't considered prime.

[@pepebriguglio6125]

Mageknight, you're right. c = sqr(2) in the special case where a = b = 1, so if they say all pythagorean primes come in the form 4n+1, then I guess they add the condition that "a is not equal to b", or in other words: the triangle must be a half rectangle, except for the special case where the rectangle is a square.

[@s0ftwrld22]

does a triangle only have two sides?

[@michaelbayer5887]

... u can go also to state delaware - the First state of Amerika - the mountain so high - 137 the lowest high mountain Position in Delaware called - Ebright Azimuth - its like Gate to the STARS.

[@_N0_0ne]

Thank you

[@treymedley]

I'm assuming you're referring to the sums thatyield a pythagorean prime. (Such as 1^2 +4^2= 17. In this example neither integers are primes. A Pythagorean prime is the sum of two *integers* squared, not necessarily two primes that are squared.

[@stumbling]

"Also it's square root is not an integer",prime numbers don't have integral square roots because they are non-divisible (hence the fact they are primes). Ten doesn't have an integral square root, but the reason it isn't a prime is that it's the product of two primes (2 and 5). Only numbers that can't be reduced to smaller "parts" are primes, they are the building blocks of all numbers. The number one doesn't count in this sense because dividing by one doesn't reduce the number to smaller parts.

[@chrisofnottingham]

5:00 Its *square* is a Pythagorean prime. I'm probably the millionth person to post this.

[@ChikoWhat]

Hey Numberphile, I remember there were combinations of A and B where B=A+1 (1 different to A) Though I forgot how to find them. The easiest example of course is if A=3 so B=3+1=4 and so C=5 :D

[@dance1211rec]

I always wanted to know if you can make a right angled triangle with these primes making up the edges

[@tompurcell1499]

Just to say that every positive integer k of the form 4n+1 can be expressed as the sum of two squares provided that a) the prime factorisation of k consists only of primes of the form 4n+1 or b) if the prime factorisation of k consists of any primes of the form 4n+3, then each such prime factor must be of a power having an even exponent. p = 4n+3 gives p² = 4(4n² + 6n + 2) + 1 which is of the form 4n+1 Given the possible remainders on division, the integer z = x² + y² can be of the form 4n, 4n+1 or 4n+2 but it is impossible to arrive at c = 4n + 3 This explains why 21 = 3 *7 cannot be expressed as the sum of two squares; each prime factor has odd exponent 1. However, if you consider 45 = 3² * 5 for example then 45 = 3² (1² + 2²) = (3² + 6²) = 45 Assuming that an integer can be expressed as the sum of two squares, the number of ways it can be so expressed, depends on the number of prime factors (up to exponent) which are of the form 4n+1. Any prime factors p^2r with p of the form 4n+3 are discounted in the calculation since their product is simply factored into each particular expression involving the former primes, with primes of the form 4n+1 being expressed as the sum of two squares in only one way. For instance, all positive integers k with prime factorisation k = pq (where each of p and q are congruent to 1 modulo 4) will have two ways of being expressed as the sum of two squares. For example 65 = 1² + 8² = 4² + 7² This comes from the fact that if P and Q are primes (of the form 4n+1, naturally), then since we can write P = a² + b² and Q = c² + d² PQ = (a² + b²)(c² + d²) = (ac + bd)² + (ad - bc)² - the sum of two squares But we could also have PQ = (a² + b²)(d² + c²) = (ad + bc)² + (ac - bd)² which gives the two expressions. so 5*13 = (1² + 2²)(2² + 3²) = (1*2 + 2*3)² + (1*3 - 2*2)² = 8² + (-1)² = 8² + 1² and 5*13 = (1² + 2²)(3² + 2²) = (1*3 + 2*2)² + (1*2 - 2*3)² = 7² + (-4)² = 7² + 4² (I think I got a little carried away here......)

[@ElusiveCube]

2 is a first P# hence it only can be divided by 1 or it's self

[@JotteXD]

137 Its something special about that number i see it occur many times a day for example 15-20 times while others only does like 1-5 for me

[@viktor1098]

He says 11^2+4^2=137 is a pythagorean prime(which it is ofc) and he does not give any specific reason to why he picked 11 and 4 as cathetuses so i am guessing you could use any integers(this is where i am confused). If you then use 3 and 1 you will get 10 as what he calls a pythagorean prime because 3^2+1^2=10. 10 is not any kind of prime as we all know.

[@gb_gabo]

My birthday is the same as his! And now I know it's made of two pythagorean primes :D

[@judmcc]

Another interesting thing about 5, 13, and 137 and being born on that day is that in years that aren't leap years, the 13th day of the 5th month is the 137th day of the year (and my anniversary) !

[@fiiredark]

But May 17th is the 137th day of the (non-leap) year… am I missing something here?

[@judmcc]

@@fiiredark Whoops, you are right. May 17 is my anniversary.

[@VictorAndScience]

Professor Laurence has really pretty numbers!

[@bxdanny]

While the triangles he shows have only the square roots of these "pythagorean primes" for their hypotenuses, they seem to be numbers that can themselves be the hypotenuse of a right triangle with integer sides (5 for 3/4/5, 13 for 5/12/13, etc.) I'm wondering if this is always true.

[@TestTubetheUnicorn]

Please do, I'd love to know.

[@numberphile]

Welsh understatement!

[@anticorncob6]

Here's something else about the numbers 5 and 13: 5 is the number of platonic solids & 13 is the number of Archimedean solids! Both very closely related.

[@Simoss13]

Born in May 13 and 137 years old :)

[@CaseyShontz]

Simoss13 if he ever turns 137 that will be his favorite birthday

[@IzzyisDizzyandFizzy]

I'm a Pythagorean prime baby!!!

[@BearArcade]

Thanks for the great video!

[@APMathNerd]

Yes it would... Side lengths 1, 1, and √2. It's an isosceles right triangle.

[@JonathanTot]

quote:"a pythagorean prime (PP) is a prime of form 4n+1" i found this definition a number of different places on the web

[@Shanack1]

I would like to know if there is something special about solitaire, and or why we set it up as we do, unless its not special.

[@smartdoctorphysicist3095]

Hi thank you for this great inside on math I wish I was as smart has this prof.

[@RiyadhAlDuwaisan]

Both of which # are : Fibo.seq + Primes

[@Madzarzour]

What other channels? I'm only subscribed to this one and Minute Physics.

[@IceMetalPunk]

If a^2 + b^2 = c, and a and b are integers, and c is prime, then c is called a "Pythagorean prime" because it matches the form of the Pythagorean Theorem.

[@sonjaklisch]

Would this work? Let's say c=5 (in a^2+b^2=c^2) 5^2= 25 and 25 is 16+9 which are both square numbers. then 13^2=169=144+25 (both square numbers) then 17^2=289=225+64 (square numbers yet again) and another one 29^2=841=400+441. Does this have a link with the Pythagorean numbers, or has someone already discovered this (probably): )?

[@hooliaw]

nice video Brady! but i thought 1 is not a prime number (as said in one of ur video)?

[@stumbling]

I don't know how I missed the middle part of your comment but I did. I still don't see where he says 10 is a prime though.

[@TheMdc78]

right which would make the actual length of the side some odd decimal number, but the square of that number is 17 so the OP is correct, they misspoke

[@hoddie54]

Taxi Cab numbers next please :)

[@WrathofRS]

He has very neat writing.

[@VWftw82]

I suddenly realized that 149 (7^2+10^2) and 181 9^2+10^2) are Pythagorean primes. Judging from that list, they seem quite common.

[@Thadddddaeus]

could you make a video about Euler's number?

[@davidwilkie9551]

Interesting, and related to e-Pi-i quantization(?), ..tangential prime.

[@bonesplitter1337]

137 is also the rounded down golden ratio (in degrees) :)

[@CRISNCHIPS12398]

Very interesting!

[@cb01023]

My results are curiously exacts and no many computes are required.Consider each number separetly.Parity is primordial.For ex. the parity of number of digits,the parity of last digits, and so on.The sum of them and parity.The digit currently test is prime number? It,s works likes a zero.

[@tommooe4524]

Didn’t understand it but it is entertaining

[@PrimusProductions]

Is 65 the only number that is the hypotenuse (the biggest side/number, c) of more than 1 Pythagorean triples?

[@Rafamegaesperto]

Primus Productions No. For example: (7,24,25) and (15,20,25)

[@jesusthroughmary]

So if a and b are consecutive Fibonacci numbers, a^2 plus b^2 always equals a Fibonacci number?

[@hkyeung1992]

I remember that I got 137 marks (out of 200) in physics exam 2 years ago. XD