An Exploration into the Statistics of Pi and other Constants

This article demonstrates how the timeline presented by the Mayan ruler K’inich Janaab’ Pakal correlates with Pi and other constants of nature. We will also explore numbers presented in the Bible.

7920, 40, and 1260 are the numbers used by the timeline. We will also explore the following numbers from the Bible:

The following numbers are foundational to this research:

232 and 1459 (the 232nd prime) -- 232 + 459 = 691
262 and 1667 (the 262nd prime) -- 262 + 667 = 929

One of the most important reasons that 1459 and 1667 are useful is because they follow an aspect in our ordered primes list. 59 is the 14th ordered prime while 67 is the 16th ordered prime.

As 8/29/2019 is known for being the start of "42 months", it's highly interesting that its long count is "13.0.6.14.2", as 61 is the 42nd sorted prime.

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Pi: 3.14159
Phi: 1.61803
e: 2.7182
2Pi: 6.28318
.
Euler-Mascheroni's Constant: em (0.5772)
Glaisher-Kinkelin's Constant: A (1.28242)
Catalan's Constant: cat (0.9159)
Khinchin-Levy's Constant: KL (1.18656)


We will be using the following timeline (image):


We can show that 7920, 40, and 1260 all relate to 14159. This is the first five digits of Pi.

14159 * 2 equals 28318, a number which first occurs in Pi at the end of 12600 digits. When summing those 12600 digits of Pi you get 56636 which is 14159 * 4.

When searching for doubled primes in Pi, 28318 (the 1667th prime * 2) is the first doubled prime to satisfy the fact that the digits leading up to and including its first occurrence in Pi, sum to a multiple of the prime. We show that using this program.

(Pastebin) - Doubled primes with digit sum multiple of the prime

Pi:	[1667] 14159 {28318}
e:	[3] 5 {10} — [5] 11 {22} — [354] 2383 {4766} — [1396] 11597 {23194} — [4377] 41879 {83758}

Now, 3069 digits of Pi precede the first occurrence of 7920 and sum to 14159.

I also see that 14159 + (14159 - 1459) or 26859 digits precede the second occurrence of 7920 in Pi.

(Pastebin) - Immediate Circular Routes in Constants:

Pi:	40, 71
Phi:	356, 487, 1601, 14145
e:	27785, 45779
em:	1, 5, 23, 51

KL:	16608, 40244

40 and 71 are unique numbers in Pi. 40 first appears in Pi at the end of 71 digits and 71 first appears in Pi at the end of 40 digits.

7140 shows us the start of the 1150 days. 11/12/1997 + 7140 days = 5/31/2017.

The string 9069 occurs at the end of those 3069 digits of Pi. 9069 - 7140 = 1929, which is 262 + 1667.

7140 has additional relations to 14159:

4071 first appears in Pi like so: 4071 12700

12700 = 14159 - 1459. This is an interesting number which shows us other circular numbers:

1601 digits precede the first occurrence of 12700 in Phi.

In the Euler-Mascheroni Constant we see that:

1112 is code for the start of the 7920 days.

1112 digits of Pi sum to 4998 (9069 - 4071). 12700 digits precede the first occurrence of 1112 in Pi. 12700 - 1112 = 11588 and 1112 first appears in Phi like so 1112 11588.

If you find the first two numbers in Pi that have a first occurrence at a location which adds up to 12700, you get this:

Program example

It's interesting that 8235 (+1) digits precede the first occurrence of 6042 in e because 1459 first appears in Phi at the end of 6042 digits.

Timeline date 12/21/2012 takes place 5518 days after 11/12/1997. 5518 can be seen as 12700 - 7182 (first four digits of e).

3069 first appears in e like this: 3069 6977 (14159 - 7182 = 6977).

And here's another example:

14145 + 71 = 14216 and 14216 first appears in Pi at the end of 71400 digits.


Here is a short timeline example to give you appreciation for the number 2961:

(Wolfram MathWorld) - Constant Digit Scanning (program):

Pi:	0, 68, 483, 6716, 33394   locations, (32, 606, 8555, 99849, 1369564)
Phi:	5, 55, 515, 0092, 67799   locations, (22, 769, 5818, 93909, 1154765)
e:	6, 12, 548, 1769, 92994   locations, (20, 371, 8091, 102127, 1061612)
em:	8, 18, 346, 2778, 84514   locations, (16, 658, 6600, 91101, 1384372)
2Pi:	4, 36, 869, 1590, 58393   locations, (16, 491, 7918, 115912, 1332503)

In this list we see 483 is the last 3 digit number to have its first occurrence in Pi. This means 483 first appears in Pi at the end of 8555 digits.

The reason Daniel broke up his 70 weeks into 7 + 62 + 1 weeks is because 483 is 69 weeks.

2184 first appears in Pi at the end of 1740 digits. 2184 + 1740 = 3924.

(Pastebin) - Numbers with a location which is double their value:

Pi:	5, 19, 94, 619, 61512
Phi:	1, 3, 8, 331, 519, 1129, 44905, 49229, 66762
e:	1, 2, 636, 637, 190853
em:	2, 8, 12, 8403, 08403, 46466, 51309, 71069, 77172
2Pi:	92, 7084, 7212, 13485, 45163, 92165

(Pastebin) - Self-locating Numbers (numbers in brackets are immediately self-locating):

Pi:	[1], [315], 360, 384, [1045794]
Phi:	8, [20], 62, [466], [4854], 46914, 48949
e:	62, [3999], 340616, [350954], [776064], [1382603], [1898195]
em:	76, [601], [5621], [6716], 7803, 90727, 92831, 8922261
2Pi:	[3], 79, [470], 816, 62180, 92253, [1493476]

(5 + 19 + 94 + 619) + (1 + 3 + 8 + 331) + (1 + 2 + 636 + 637) = 2356

An interesting fact about 11740 is that it first occurs in Pi at the end of 424777 digits, the first 6 digits of 3 Pi.

An example with 11740:


6716 is a constant digit scanning number from Pi and also a self-locating number in Euler-Mascheroni's Constant:

12/21/2012 has a relation to 5/14/1948 through the concept of constant digit scanning:

Circular Numbers

40 and 487 are two circular numbers which are used in the timeline:

If you use 7473 and our two circular numbers:

The circular number of Khinchin-Levy's Constant constant also has a relation to 8316:

I see that:

Constant Digit Scanning and Self-Locating Numbers in Euler-Mascheroni's constant

32 + 606 + 8555 = 9193

9193 + 6042 = 15235

9193 - 6042 = 3151. 3151 digits of Pi precede the third level digit scanning location of em: 6600

7917

7917 is a number which can represent the crucifixion of Jesus as 7/17/2019 + 3 days = 7/20/2019.

8555 - 606 - 32 = 7917

7917 first appears in Pi at the end of 1789 digits. The first 232 of Pi occurs in this location: 232 7917 8608 (7917 + 691 = 8608).

7917 + 1789 = 9706, which occurs here: 1459 1028 9706. This is the first occurrence of 1459 in Pi.

An apparent balancing point

929 first appears in Phi at the end of 1393 digits.

Constant Digit Scanning

If you sum the first four levels of Constant Digit Scanning numbers you will find they have a relation to circular numbers.

0 + 68 + 483 + 6716 = 7267

7267 digits precede the first occurrence of 1601 in Pi.

6 + 12 + 548 + 1769 = 2335, and 2335 digits precede the first occurrence of the string 42163 in e:

2335 is associated with circular numbers, and so the following example is interesting:

The reverse of 4359 is 9534, which is interesting as 9534 first appears in Pi at the end of 667 digits.

Now for Phi:

5 + 55 + 515 + 0092 = 667, and 667 digits precede 400 in Phi. (40)

So we see that Pi hones in on 1601 while Phi hones in on 40.

1601 + 40 = 1641

12700 + 1641 = 14341, and 14341 digits of e precede the second occurrence of 1667.

We can make interesting timeline alignments with the number 1667:

Notice that 1590 digits precede the first occurrence of 1667 in e. This is the constant digit scanning number of 2Pi. This shows us that 1667 and 6716 have a relation to each other through the concept of ordered primes.

(0 + 68 + 483 + 6716) + (5 + 55 + 515 + 0092) + (6 + 12 + 548 + 1769) = 10269


Below we show our ordered primes list. Example: 67 increases 9.83% from 61, the prime before it.

Notice that 1459, 1541, and 1667 appear consecutively by concatenation of the list number with the prime.

The primes of these numbers, 12203, 12941, and 14159 are also important:

List:

1|2, (?)
2|5, (66.6666666667%)
3|11, (57.1428571429%)
4|3, (50.0%)
5|7, (40.0%)
6|17, (30.7692307692%)
7|29, (26.0869565217%)
8|23, (21.0526315789%)
9|37, (19.3548387097%)
10|13, (18.1818181818%)
11|53, (12.7659574468%)
12|127, (12.389380531%)
13|19, (11.7647058824%)
14|59, (11.320754717%)
15|41, (10.8108108108%)
16|67, (9.83606557377%)
17|47, (9.3023255814%)
18|97, (8.98876404494%)
19|79, (8.21917808219%)
20|89, (7.22891566265%)

1541 is special because it first appears in Pi at the end of 5280 digits. (2640 * 2 = 5280, and 2640 * 3 = 7920)

Diagonal numbers on this list are also significant:

1847 first appears in Pi at the end of 27920 digits. Then, 2640 first appears in Pi at the end of 2079 digits. Note that 20 and 79 can be reversed to form 7920.

2640 digits of Pi precede the first occurrence of 6829, the 879th prime. 6829 can be used like so:

879 and a seeming connection to 14159

879 digits is an interesting point of alignment in constants:

In the next section we'll review 1459 and will look at additional examples of the importance of ordered primes.

If you look at 59 and 14 instead you get:

5280 first appears in Pi like this: 5280 1735. 7015 is formed by adding 5280 to 1735.

1599 is considered an important number in the Pi code. For example:

And a confounding alignment which we see:

More Creations

7/26/2020 is formed through the use of 1740.

11/12/1997 + (1740 + 2184) + 2184 + 2184 days = 7/26/2020. There are 8292 days here total.

(Pastebin) - Numbers with a match of location and digit sum:

Pi:	53, 103, 1693, 4159, 5923, 75533
Phi:	3, 281, 203183
e:	3547, 15401

This list displays the following property:

12700 is important here: 12700 first appears in e at the end of 15401 digits.

15401 - 12700 = 2701, the value of the first verse of the Bible. This creates the timeline date 5/14/2020. 12/21/2012 + 2701 days = 5/14/2020.

I found this property: 5/14/2020 - 12700 days = 8/6/1985.

5/14/1948 -> 8/6/1985 = 13598 days

5/14/2020 - 15401 days = 3/15/1978 and 3/15/1978 -> 11/12/1997 = 7182 days.

When we pick 4159 and other 4th numbers from our statistics lists:

11597 + 6716 + 4159 = 22472, and 22472 digits precede the first occurrence of 1740 in Pi.

This is interesting as numbers like 929 and 2294 align in special ways across many different constants:

929 is formed through 1667 and 262. As we see 6716 here, it's interesting, as it seems to have a relation to ordered primes.

A very interesting Timeline Example

5/14/1948 + 61803 days (first five digits of Phi) = 7/30/2117 (13.5.6.2.6)

Here's a reminder about the number 1459:

The ordered prime 1459 connects us to 1667 and 6716.

We can show that Glaisher-Kinkelin's Constant (A) also ties into this:

We mentioned 879 in Pi above. 879 digits of Pi sum to 3911.

In other articles we've shown:

The 2860th prime is 25999. 5/14/1948 + 25999 days = 7/20/2019.

8292 + 3911 = 12203, the 1459th prime.

3911 and 3924 are complimentary numbers:

42

42 is an interesting number sometimes associated with the occult. It first occurs in Pi like so: 253 42 117

Every digit of Pi before 42 sums to 440. This creates the timeline date 11/11/2020. 8/29/2019 + 440 days = 11/11/2020.

108 is a number associated with the Hindu Gods. 93 first appears in Pi at the end of 15 digits. 93 + 15 = 108.

3069 - 42 - 93 = 2934

2934 first appears in Pi at the end of 7918 digits (a constant digit scanning location of 2Pi).

An interesting timeline example:

Continue reading the 42 Essay

More Statistics

(Pastebin) - Prime (#) double Location Search:

(Pi)    71 (prime #20) first appears in Pi at the end of 40 digits
        359 (prime #72) first appears in Pi at the end of 144 digits

(Phi)   43 (prime #14) first appears in Phi at the end of 28 digits

(e)     85781 (prime #8346) first appears in e at the end of 16692 digits

85781 is interesting as 5781 first appears in Pi next to the second 14159: 14159 5781.


Another timeline example:

The first 262 decimal digits of Pi, Phi, e, (and the Euler-Mascheroni constant) each sum to 1192.

1717:

11/12/1997 + 7110 days = 5/1/2017

An interesting concept:

1667 first appears in em at the end of 10302 digits.

7

2383 and 11597 are in our list "Doubled primes with digit sum multiple of the prime".

483 is 7 less than 490, the number of the 70 weeks. Add 7 to the 3 digit constant digit scanning number of Phi:

Speculation

(5 + 19 + 94 + 619) + (1 + 3 + 8 + 331) + (1 + 2 + 636 + 637) + 0 + 68 + 483 + 6716 = 9623

Using the 42, 93, 135 Test, we see: 8374 first appears in Pi at the end of 1249 digits. 8374 + 1249 = 9623. (Reverse: 4738 + 9421 = 14159)

As 1667 is important, I've also noticed that 14293 is important, the 1677th prime. (14293 digits of e precede the first occurrence of 4159)

4/10/2020 -> 11/11/2020 = 215 days. 215 (or 4215) first appears in Pi at the end of 3100 digits. 3100 digits of Pi sum to 14293.

(oeis) - Numbers n such that digits of prime(n) end in n:

7, 9551, 303027, 440999, 968819

14186 first appears in Pi at the end of 99551 digits, and 99551 is the 9551st prime.