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Post by dividavi on Jul 18, 2018 2:06:29 GMT
Here's a great equation that almost seems to mean something. It reads this way: Pi to the 4th plus Pi to the 5th is about equal to e to the 6th. Both sides are about equal to 403.
π^4+π^5~e^6
Repunit primes
Primes containing only the decimal digit 1.
11, 1111111111111111111 (19 digits), 11111111111111111111111 (23 digits) (OEIS A004022)
The next have 317, 1031, 49081, 86453, 109297, 270343 digits (OEIS A004023)
Ramanujan and Taxi 1729
1729 is the natural number following 1728 and preceding 1730. It is known as the Hardy-Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation:[1][2][3][4]
The two different ways are:
1729 = 1^3 + 12^3 = 9^3 + 10^3
I thought I was the first to discover the wondrousness of the number 1006301. It's the initial member of two prime quadruples with the smallest possible difference of 30. Numbers n such that {n, n+2, n+6, n+8, n+30, n+32, n+36, n+38} are all prime. Turns out I wasn't the first.
Here's a list of such numbers:
1006301, 2594951, 3919211, 9600551, 10531061, 108816311, 131445701, 152370731, 157131641, 179028761, 211950251, 255352211, 267587861, 557458631, 685124351, 724491371, 821357651, 871411361, 1030262081, 1103104361
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Post by Aj_June on Jul 18, 2018 4:05:57 GMT
Here's a great equation that almost seems to mean something. It reads this way: Pi to the 4th plus Pi to the 5th is about equal to e to the 6th. Both sides are about equal to 403. π^4+π^5~e^6 Repunit primesPrimes containing only the decimal digit 1. 11, 1111111111111111111 (19 digits), 11111111111111111111111 (23 digits) (OEIS A004022) The next have 317, 1031, 49081, 86453, 109297, 270343 digits (OEIS A004023) Ramanujan and Taxi 17291729 is the natural number following 1728 and preceding 1730. It is known as the Hardy-Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation:[1][2][3][4] The two different ways are: 1729 = 1^3 + 12^3 = 9^3 + 10^3 I thought I was the first to discover the wondrousness of the number 1006301. It's the initial member of two prime quadruples with the smallest possible difference of 30. Numbers n such that {n, n+2, n+6, n+8, n+30, n+32, n+36, n+38} are all prime. Turns out I wasn't the first. Here's a list of such numbers: 1006301, 2594951, 3919211, 9600551, 10531061, 108816311, 131445701, 152370731, 157131641, 179028761, 211950251, 255352211, 267587861, 557458631, 685124351, 724491371, 821357651, 871411361, 1030262081, 1103104361 I like the almost magical properties of the Golden ratio and its close link with Fibonacci sequence.
1.61803... = 1 + 1/1.61803...
Technical analysts (while I believe technical analysis is voodoo of finance and total nonsense) also use golden ratio and Fibonacci series in determining directions of stock price movements and estimated reversals.
Researchers have found that even great pyramid of Giza might be related to the golden ratio.....My favourite series of wonders will always be 0 1 1 2 3 5 8 13 21 34 55 89.....
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Post by Aj_June on Jul 18, 2018 23:57:41 GMT
Linking Kondratieff Waves with Fibonacci series.
Unfortunate Russian Economis Nikolai D. Kondratieff first brought to attention the economic cycle of 54 years which repeats all over after approximately 54 years. Each cycle consists of growth, stagnation and recession. Stagnation period could represent periods of prosperity.
While searching for relations between Kondratieff waves and Fibonacci I found this on a website:
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Post by koskiewicz on Jul 19, 2018 1:22:36 GMT
...all numbers, however large, can be broken down to a single numerical digit (1 though 9).
For instance, the number 46,778 = 5.
4 + 6 = 10, + 7 = 17, + 7 = 24, + 8 = 32...3 + 2 = 5
You can turn this number (46,778) topsy turvy and any which way you want, and the end result of this will always be "5"...
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Post by general313 on Jul 19, 2018 15:35:43 GMT
Here's a great equation that almost seems to mean something. It reads this way: Pi to the 4th plus Pi to the 5th is about equal to e to the 6th. Both sides are about equal to 403. π^4+π^5~e^6 Repunit primesPrimes containing only the decimal digit 1. 11, 1111111111111111111 (19 digits), 11111111111111111111111 (23 digits) (OEIS A004022) The next have 317, 1031, 49081, 86453, 109297, 270343 digits (OEIS A004023) Ramanujan and Taxi 17291729 is the natural number following 1728 and preceding 1730. It is known as the Hardy-Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation:[1][2][3][4] The two different ways are: 1729 = 1^3 + 12^3 = 9^3 + 10^3 I thought I was the first to discover the wondrousness of the number 1006301. It's the initial member of two prime quadruples with the smallest possible difference of 30. Numbers n such that {n, n+2, n+6, n+8, n+30, n+32, n+36, n+38} are all prime. Turns out I wasn't the first. Here's a list of such numbers: 1006301, 2594951, 3919211, 9600551, 10531061, 108816311, 131445701, 152370731, 157131641, 179028761, 211950251, 255352211, 267587861, 557458631, 685124351, 724491371, 821357651, 871411361, 1030262081, 1103104361 I like the almost magical properties of the Golden ratio and its close link with Fibonacci sequence.
1.61803... = 1 + 1/1.61803...
Technical analysts (while I believe technical analysis is voodoo of finance and total nonsense) also use golden ratio and Fibonacci series in determining directions of stock price movements and estimated reversals.
Researchers have found that even great pyramid of Giza might be related to the golden ratio.....My favourite series of wonders will always be 0 1 1 2 3 5 8 13 21 34 55 89.....
Three perpendicular golden rectangles generate all of the vertices of an icosahedron (also a consequence of the relation between pentagons, icosahedrons and dodecahedrons).  |
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Post by cybajedi on Jul 19, 2018 17:16:01 GMT
Nerds.
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Post by Aj_June on Jul 19, 2018 19:54:27 GMT
I like the almost magical properties of the Golden ratio and its close link with Fibonacci sequence.
1.61803... = 1 + 1/1.61803...
Technical analysts (while I believe technical analysis is voodoo of finance and total nonsense) also use golden ratio and Fibonacci series in determining directions of stock price movements and estimated reversals.
Researchers have found that even great pyramid of Giza might be related to the golden ratio.....My favourite series of wonders will always be 0 1 1 2 3 5 8 13 21 34 55 89.....
Three perpendicular golden rectangles generate all of the vertices of an icosahedron (also a consequence of the relation between pentagons, icosahedrons and dodecahedrons). Wow...Seems like I get know a new application of golden ratio every day! |
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Post by phludowin on Jul 21, 2018 7:11:08 GMT
Take the number 333666.
Its next multiples are 667332 and 1000998.
If you add 1 to each of these numbers you get three primes.
When you multiply these primes 333667, 667333 and 1000999, you get a Carmichael number.
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Post by Aj_June on Jul 21, 2018 7:21:19 GMT
Take the number 333666. Its next multiples are 667332 and 1000998. If you add 1 to each of these numbers you get three primes. When you multiply these primes 333667, 667333 and 1000999, you get a Carmichael number. Wow...a large number and it's next 2 multiples lie so close to prime numbers. This fact alone is pretty astonishing. Even though there is no largest prime number, prime numbers become scarce as you count high. |
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