Dear all,
Let us look at the first 1,000 digits of PI as below
3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999837297804995105973173281609631859
50244594553469083026425223082533446850352619311881
71010003137838752886587533208381420617177669147303
59825349042875546873115956286388235378759375195778
18577805321712268066130019278766111959092164201989
I have an interesting finding. This series can be fragmented into CONSECUTIVEprime or Fibonacci numbers.
First of all, we have the first 4 digits 3141. This is a prime.
Next to it is 5926535897, which is also a prime. Similarity, the next prime value is 93238462643, and so on etc.
In next step, I reversed this 1,000 digits of PI as below
98910246129095911166787291003166086221712350877581877591573957873532883682659511378645578240943528953037419667717160241838023357856882578387313000101718811391625305864433528032252462038096435549544205958136906182371379501599408792738999999431127078150699031774779263189518144304680691209212116599102453298529869722970501735859456410343594221090448641278717363719069877572431775877280653625417218650002315049667648184764832576713926717129350772073490689712070917374225936494931206803466560442633763389219491103818397221984272575881537659472699732644708458115013971162391837116812903591959575630727503349061151491596414831256640288450350331100630952987634635171904529282690290251884718855136066007854273721419420627063933128466234540168430643296658465419091021725613876873328465748216443395665790188244691830394598492264469555011258391072014820547111848218049535271322850559064483907466032823156808412897607112435284308268998026826046187032954494790285015739939617914882059723833462648323979853562951413
It is interesting that I am successful when doing the same analysis. The first prime string here is
989102461290959111
And the second one is
667872910031 etc.
You can view my detail calculation in file PI-Prime.docx which has been shared for everyone in my google drive
https://drive.google.com/drive/u/0/folders/0BzAetX6K_uyALUc2ZnkzV2xaTkE
My investigation can be used for further researching with more digits of PI, for example 2000, 3000, or 100,000 digits.
All of your feedback are welcome.
Thank you
Thinh Nghiem
Hello Thinh,
I don't want to discourage you from your research but consider a string of randomly chosen integer values {a_1,a_2,...,a_1000}from interval which form the number a_1a_2...a_1000, f.e. {1,6,3,...,5} would result in number 163...5. You will notice that by taking appropriate number of digits you will always find a prime number within this string. So it is not only the pi feature to contain prime numbers within it. Unless you found some regularity concerning the primes itself or the number of digits gathered from consecutive primes that creates some series or something similar.
Good luck in your findings!
BR, Piotr
Random sequences carry no information. But Pi and its fragments do carry information. The message is that of an irrational number.
I just wonder why it is not just 3 taken as the first prime number and 14159 as the second one. Despite thsi, the randomness of the obtained sequence of primes is also interesting!
BR, Joachim
Dear Thinh,
We can simplify your idea as the following:
Is there any common pattern between
(1) The expansion of the irrational number pi (up to x digits)
(2) The Fibonacci sequence ( maybe Fibonacci type sequence)
(3) The prime numbers.
Each term is interesting by itself (1) pi to represent the ratio of the circle perimeter to its diameter; this number plays an important rule in all branches of science. (2) The most popular sequence of fascinating properties, the average of its terms converge to the golden ratio.(3) The primes and their distribution that full of mysteries.
The General answer seems to be very difficult but the limitation of 1000 digit, may bring partial answers which can be discovered by inspection.
For example, 141592653589 is prime followed by 79323846264338327 is prime followed by the prime 9502884197169399375105820974944592307
and you proceed to find a chain of primes.
Best wishes
To @Piotr Ptak, @Peter Breuer
Yes, you are right. My method can be applied for any irrational number like sqrt(2), as @Jerry Decket mentioned. What I want to show here is we can dig deeply into the PI value, which has been mysterious for centuries, by using my way.
a pi are randomness
As far as anyone knows, the digits of pi are (pseudo-)random. They pass any statistical test for randomness you care to throw at them.
Indeed, as you mentioned, that is typical of the digits of any irrational number at all [Several good pseudo random number generators work by repea
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