Tuesday, 20 October 2020

33rd Black Monday Anniversary: Fibonacci, Prime & Perfect Numbers

 The Dow fell 410.89 points on Monday (October 19) as investor hopes for a new stimulus package dwindled.

  • 1, 1, 2 and 3 are the first four terms in the Fibonacci sequence.
  • Joining each number forms 1123, the 188th prime number.
  • 2, 3 and 5 are the first three prime numbers.
  • Joining these three numbers forms 235.

Prior to the 2020 market crash, the largest daily change in the Dow's history was 1175 points on February 5, 2018.  This record was broken when the Dow fell 1191 points on February 27, 2020.

  • From February 5, 2018 to October 19, 2020 is 987 days.


  • 987 is the 16th Fibonacci number.


  • From February 27, 2020 to October 19, 2020 is 235 days.



  • The 235th prime number is 1483.



1483 - (987) = 496 (the 3rd perfect number)


  • 1248 is the number to which 235 must be added to reach the 235th prime number.

1248 + (235) = (1483)


1123 + (125) = 1248

1248 + (235) = (1483)


  • November 23 (11/23) leaves 38 days remaining in the year.
  • The 38th prime number is 163.
  • 125 is the number to which 38 must be added to reach 163.

  • October 19, 2020 is the 33rd anniversary of the Black Monday crash [(10/19)/'87].
  • February 27, 2020 is the 87th anniversary of the Reichstag fire (2/27/'33).

  • The 87th prime number is 449.
  • The 33rd prime number is 137.
  • The 137th prime number is 773.
  • 1019 is the 171st prime number.

  • 362 is the number to which 87 must be added to reach 449.
  • 848 is the number to which 171 must be added to reach 1019.
  • 935 is the number to which 188 must be added to reach 1123 (the 188th prime number).
  • On the 33rd anniversary of Black Monday the Dow fell 411 points.

848 + 362 + (38) = 1248

848 + 87 = (935)

411 + (38) = 449


  • 137 is a divisor of 411: 411/3 = 137.


411 + 362 = 773 (the 137th prime number)


411 - 163 = 248

  • 248 is a divisor of 1488 and 496.

362 - 248 = 610 (the 15th Fibonacci number)

  • The number-prime relationship (65, 313) can be represented by simply writing 248, since 248 is the number to which 65 must be added to reach 313.
935 + (313) = 1248

[Note also, the divisors of 1175 sum to 1488.  The difference between 1175 and the sum of it's divisors is 313.]



87 + 33 + (17) = 137 (the 33rd prime)

87 - 33 = 54

  • The 54th prime number is 251.
  • The 251st prime number (1597) is the (17)th Fibonacci number.
  • 1346 is the number to which 251 must be added to reach 1597.

1346 + 137 = 1483

1346 - 411 = 935

137 + 235 = 372

  • 89 is the 11th Fibonacci number.
  • 372 is the number to which 89 must be added to reach 461, the 89th prime number.
  • The difference between 171 and the sum (260) of it's divisors is 89.

260 - 171 = 89



1346 + 125 = 1471 (the 233rd prime number)

  • 233 is the 13th Fibonacci number.
  • 1471 + (17) = 1488

  • 28 is the 2nd perfect number.
  • 6 is the first perfect number.

411 - (28 + 6) = 377

  • 377 is the 14th Fibonacci number.
  • Joining 28 and 6 forms 286.

286 + (125) = 411


(773 - 137) + 235 = 871

871 + (377) = 1248






Monday, 5 October 2020

Dark & Recursion: Largest Single Day Changes (11, 66, 89)

"Dark" and the novel "Recursion" are similar in that they are both philosophical on the nature of time.  In Dark the apocalypse occurs on June 27, 2020 as depicted in "Endings and Beginnings," the final episode of season 2.  In Recursion the world disintegrates on April 16, 2019.
  • The two dates are 438 days apart.

The 438th prime number is 3061:


2623 is the number to which 438 must be added to reach 3061:

2623 + (438) = (3061)


The largest point drop in the Dow's history prior to the 2020 market crash was 1175 points on February 5, 2018.  This record was broken on February 27, 2020 when the Dow fell 1190.95 points.

Consider the trading week (beginning on February 24, 2020) in which the old record was broken:

  • February 24   (- 1031.61)
  • February 25   (- 879.44)
  • February 26   (- 123.77)
  • February 27   (- 1190.95)
  • February 28   (- 357.28)


(1032 + 879 + 124 + 1191 + 357) = 3583, the 502nd prime number.


1191 + (502) = 1693, the 264th prime number.


From April 16, 2019 to February 27, 2020 is 317 days:


From February 27, 2020 to June 27, 2020 is 121 days:


  • 317 is the 66th prime number.
  • 66 is the 11th triangular number.

  • 121 is 11 squared.
  • 89 is the 11th Fibonacci number.
  • The 89th prime number is 461.
  • 372 is the number to which 89 must be added to reach 461  372 + (89) = (461).
  • 372 + (66) = 438
  • Prior to February 27, 2020 the difference between the largest point drop (1175) and largest point gain (1086) in the Dow's history was 89.

1693 + (89) = 1782

  • The 317th prime number is 2099.


  • 1782 is the number to which 317 must be added to reach 2099.

1782 + (317) = (2099)

(1693 + 89) + (317) = (2099)

Consider the weekly net changes during the 8 consecutive trading weeks beginning from February 24, 2020:
  • February 24 to February 28   (- 3583)
  • March 2 to March 6   (+ 455)
  • March 9 to March 13   (- 2680)
  • March 16 to March 20   (- 4011)
  • March 23 to March 27   (+ 2464)
  • March 30 to April 3   (- 584)
  • April 6 to April 9   (+ 2667)
  • April 13 to April 17   (+ 523)

Recall the significance of the number-prime relationship [344, 2311] to the trading week beginning on March 16, 2020.  The difference in the net change during the trading weeks beginning on March 9th and March 16th is 11 cubed:

(4011 - 2680) = 1331 = (11×11×11)

  • 23:11 military time is 11:11 on the twelve-hour clock.
  • 2311 is the 344th prime number.

344 + [(- 3583) + 455 - 2680 - 4011 + 2464 - 584 + 2667 + 523] = 344 + [- 4749] = - 4405

Recall:
  • There are 438 days between April 16, 2019 and June 27, 2020.
  • 3061 is the 438th prime number.
  • 2623 is the number to which 438 must be added to reach 3061.
  • April 16, 2019 is 317 days before February 27, 2020 (the date the old record for the largest single-day point change was broken).
  • 317 is the 66th prime number.
  • 66 is the 11th triangular number.
  • June 27, 2020 is 121 days after February 27, 2020.
  • 121 is 11 squared.
  • 89 is the 11th Fibonacci number.
  • Prior to February 27, 2020, the difference between the largest point drop (1175) and largest point gain (1086) in the Dow's history was 89.
  • 1693 + (89) = 1782
  • 1782 is the number to which 317 must be added to reach 2099, the 317th prime number.

(2623 - 4045) = - 1782 = - (1693 + 89)


Some Additional Notes on The 2020 Stock Market Crash:


  • During the trading week beginning on February 24, the Dow fell 1191 points breaking the previous record for the largest single day loss.
  • The net change during this week was 3583 points.
  • 3583 is the 502nd prime number.
  • 1191 + 502 = 1693, the 264th prime number.

6765 is the 20th Fibonacci number:



6765 - (3583 + 502) = 2680

  • 2680 is the net change in the trading week beginning on March 9.

The 16th Fibonacci number is 987:


2680 - 987 = 1693


  • The largest point gain in the Dow's history was 2113 points on March 24, 2020.
  • 2113 is the 319th prime number.

  • 1794 is the number to which 319 must be added to reach 2113.

6765 - (1794) = (4971)


From March 24 to March 26 the Dow posted it's biggest three day rally in 89 years:
  • March 24  + 2113
  • March 25  + 496
  • March 26  + 1352

(2113 + 496 + 1352) = 3961, the reflection of 1693.

  • The three day rally began on March 24 (24/3).
  • The second consecutive gain was 496 points on March 25 (25/3)
  • 243 + 253 = 496 (the third perfect number).
  • The final day of the three day rally was March 26 (26/3).
  • 243 + 253 + 263 = 759
  • 759 is the number to which 694 must be added to reach 1453.
  • 3541 is the 496th prime number.


  • 233 is a divisor of 3961: 3961/17 = 233.
  • 233 is the 13th Fibonacci number.
  • 694 - 233 = 461, the 89th prime number.
  • 89 is the 11th Fibonacci number.

Consider the chain of Prime numbers starting at 11:


(The 11th prime number is 31  the 31st prime number is 127)


  • The 31st triangular number is the third perfect number (496).
  • The 127th triangular number is the fourth perfect number (8128).


  • The net change in the trading week beginning on April 6th was 2667 points.
  • The divisors of 2667 sum to 4096.



4096 - 2667 = (1429)

  • 1429 is the number to which 264 must be added to reach 1693 (the 264th prime number).


1429 + (264) = (1693)


Dark and Recursion: Largest Single Day Changes


  • The largest point drop in the Dow's history was 2997 points on March 16, 2020.
  • The Largest point gain in the Dow's history was 2113 points on March 24, 2020.

June 27, 2020 is 103 days after March 16, 2020:



June 27, 2020 is 95 days after March 24, 2020:


103 + 95 = (198)


April 16, 2020 is 335 days before March 16, 2020:



April 16, 2020 is 343 days before March 24, 2020:


335 + 343 = (678)


  • 198 is a divisor of 1782: 1782/9 = 198.
  • 66 is a divisor of 198: 198/3 = 66.

198 + (66) = 264


The 198th prime number is 1213:


  • 1015 is the number to which 198 must be added to reach 1213.

1015 + (678) = 1693


The divisors of 678 sum to 1368:


3061 - (1368) = 1693


  • 461 is the 89th prime number.
  • The 461st prime number is 3259.


3259 - 3061 = (198)


Consider the final trading week of the 2020 market crash:

April 6   (+ 1627)
April 7   - 26
April 8   + 780
April 9   + 286

  • The net change during the week was (+ 2667) points.
  • The largest point gain during the week was 1627 points on April 6 (6/4), the first trading day of the week.
  • 64 is 8 squared.
  • The divisors of 2667 sum to 4096.
  • 4096 is 64 squared.
  • 4096 - 2667 = 1429
  • 1429 is the number to which 264 must be added to reach 1693, the 264th prime number.

66 is a common divisor of 198 and 264:
  • 198/3 = 66
  • 264/4 = 66
198 + (66) = 264

1627 - (198) = 1429

1627 + (66) = 1693


Using the most basic cypher (ordinal), "Dark" equals 34:


The 34th prime number is 139:



1627 - (139) = 1488 = (16×93)


Adding 678 to 198 gives the reflection (876):

198 + (678) = (876)


(678 + 876) + 139 = 1693