A brief overview of the first 10 million characters of Pi

Introduction

Recently I came across this video:







In it, the British guys talk about how they printed the Pi number up to a million mark on a paper tape, and then rolled it out on the runway. It turned out the tape length of 1.69 km. For orientation in this set of digits every 10 characters is the corresponding label.



During their event, the authors tell about interesting places of Pi. So, on the 762nd symbol begins the so-called. Feynman point . The nearest sequence consisting of the same numbers, longer than this will be only 710000 digits.

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One of the commentators shared a link and added "Learn." This story is devoted to such a superficial study of the first 10 million characters of Pi.

Overview

The first thought is, of course, to count how many times units, twos, etc. meet here. Intuition suggests that the number of meetings with each digit should be about a million. Slightly less lazy readers can apply mathematical statistics techniques when processing results, but I will confine myself to the following table.

Numeral	Number of meetings
0	999440
one	999333
2	1000306
3	999965
four	1001093
five	1000466
6	999337
7	1000207
eight	999814
9	10,00040

Here, exactly in half of the cases, the number of meetings is greater than expected. Expected.



Next, let's see how often in our number there are pairs, twos, triples, etc. same numbers. The results are shown in a similar table. Eight in a row any identical numbers are not found in the considered number of characters Pi.

Numeral	Two in a row	Three in a row	Four in a row	Five in a row	Six in a row	Seven in a row
0	98638	9669	872	87	6	one
one	98689	9629	976	101	ten	one
2	98969	9775	948	84	9	0
3	99552	9831	934	87	7	one
four	98934	9583	891	87	eight	0
five	99483	9953	1006	97	eleven	2
6	98867	9599	940	96	9	one
7	99194	9780	1004	112	14	2
eight	98761	9641	911	92	sixteen	2
9	99112	9977	1005	103	17	four

From the interesting here: continuous sequences of nines are more common. And 999999 appears more often 000000 almost three times.



And finally, a brief look at what other sequences are found in Pi. So, once there is a series of 1234567 , which is the longest sequence in a row arranged in ascending order of numbers. If we look for rows of digits arranged in descending order, then the longest of them is 876543210 and it occurs once.

Instead of conclusion

Next, I decided to see how the number Pi intersects with other known constants. So, the first 6 digits of the number e (e = 2.71828) are found 7 times, like the first 6 digits of Pi himself. It would be interesting to look for intersections of known constants, but the research method applied here (Ctrl + F at pi.karmona.com ) is not suitable for this. One of the databases of known constants is oeis.org .



Thanks for attention.