20180101, 19:46  #144 
Dec 2017
32_{16} Posts 

20180101, 20:54  #145  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3×29×113 Posts 
Depends on a person!
Now, my question is this: wasn't this thread (and the poster) way better off when the thread was locked the first time? Observe: the only thing that happened after reopening was that selfflagellation continued, followed by silent mediation. Sometimes I amazed how well I can see the (not so distant) future. Quote:


20180102, 00:55  #146 
∂^{2}ω=0
Sep 2002
República de California
2^{4}·733 Posts 
@Serge: I heard the "predictions are hard" quip attributed to Yogi Berra, not Bohr. Two names I never thought I'd see come up in the same sentence. :)
Here is a detailed investigation into the history of said aphorism, which concludes that the saying is indeed most likely Danish in origin, but not due to Bohr. This sort of proliferation of attribution is quite common with especially pithy/witty sayings. To use a maths analogy, it's like people later slapping the name 'Gauss' on this, that or the other technique in order to boost its profile and/or legitimacy. (An example I recall from my days as a grad. student in fluid mechanics was something referred to as the "GaussSeidel" method, an iterative relaxation algorithm for solution of discretized elliptic PDEs. About which one of my profs commented, "Seidel didn't invent it and Gauss didn't work on it.") Last fiddled with by ewmayer on 20180102 at 01:28 
20180102, 01:08  #147 
If I May
"Chris Halsall"
Sep 2002
Barbados
24341_{8} Posts 

20180102, 01:19  #148 
Dec 2017
32_{16} Posts 
https://quoteinvestigator.com/2013/10/20/nopredict/
does it really matter who said it first ? it's funny anyway i.e. fermat is also "funny" Last fiddled with by guptadeva on 20180102 at 01:38 Reason: including reference to fermat 
20180102, 01:48  #149  
Feb 2017
3×5×11 Posts 
Quote:
Thanx for your comments, and an opportunity, to provide the derivation of my now infamous algorithm. I work with what I would call numbergrids a lot, whereby I take the postive integers, but mostly the odd numbers for obvious reasons, and arrange them into tables of varying number of columns, e.g. 01,03,05,07,09 11,13,15,17,19, 21,23,25,27,29, 31,33,35,37,39 41,43,45,47,49 51,53,55,57,59...this being a 5columngrid of odd numbers. Some interesting facts coming from this grid for example would be; 1) The columns filter the primes into primes having the same unit digit, i.e col1 having all primes ending with the digit 1, column 2 has unit digit 3, and so on. 2) The grid filters out the mutiples of 5 for a grid with 5 columns, multiples of 7 for a grid with 7 columns, etc 3) The grids have the property that per row (in a column), the values at that location, have the property of sieving out thevalue at that number of rows further down the column, e.g C1/R2 has a value of 11. All values in muliples of 11 would be composite. In C1/R2 the value is 21 and all numbers removed 21 rows from this location in the column, would be composite. Since 21 is a composite itself, with factors 3 & 7, all values removed both 3 and 7 rows from this location/value in the column would be composite as well. The rows/values not so eliminated are primes. This makes these grids de facto, primality "sieves", which could actually be formulated/algorithmized as well. When I tabulated the mersenne odd numbers vs modulo of the odd numbers (in Excel worksheets)....the quotions became bulky too quickly, I observed many interesting patterns for the results of the modulos...See extraction from the table/grid below; 01,02,03,04,05,06,07,08,09,10,11,12,13,14.......Column numbers Row M 03,05,07,09,11,13,15,17,19,21,23,25,27,29.......Odd numbers 01 01 01,01,01,01,01,01,01..........................................M mod Odd Number 02 03 01,02,00,07,07,07,07,07,07,07,07,07,07,07,07 03 05 01,01,03,04,09,05,01,14,12,10,08,06,04,02,00 04 07 01,02,01,01,06,10,07,08,13,01,12,02,19,11,03 05 09 01,01,00,07,05,04,01,01,17,07,05,11,25,18,15, etc. 06 11 01,02,03,04,01,06,07,07,14,10,00,22,22,17,11 The Mcolumn being the mersenne number 2^m1, and the other columns being M mod Odd number. From this table many weird and wonderful properties were evident; 1) The Mcolumn also has the sieve property per row as discussed above (making it a de facto mersenne primality checker) 2) Within a column the modulos repeat itself according to definite pattern commensing with 1 and ending with the column number., albeit not always with a factor due to the primality of the mersenne primes. However, the table exposes a factor for M11 at Column 11, Odd number 23, the modulo returning 00 3) The modulo of the row number equivalent vs the column number equivalent was always equal to the the row/column number itself, unless the odd number was composite! Taking this relationship of the modulo for the mersenne number of a row vs the odd number of the corresponding column, e.g. row 5, reduced to the following; Row 5 is equivalent to M9 and Col 5 is equivalent to the odd number 11, WITH the modulo = "5"...which was apparently the case for all PRIME numbers (as tabulated per column). The relationship was then, using the rule of "when the modulo of row number equivalent vs column number equivalent = row/column number being prime", gave a relationship of Mn to Odd number (n+2), when the modulo was equal to the row/column number, being prime. For row 5, mersenne prime was "9", and the associated odd number "11", with the modulo for the function being "5", "5" being the mersenne index [(9) +1]/2.... I finally the reduced this to the formula/algorithm; When 2^91 mod (9+2) == (9+1)/2, then (n+2) is prime according to the pattern that eminated from the table, Generalized, the formula became; When 2^n1 mod (n+2) == (n+1)/2, (n+2) would be prime, else composite., according to the table I was working with which I took up to about + 301 The table looked like a rosetta stone for prime numbers (for the column odd numbers) I then saw this relationship (in the table) as a relationship that defines the relationship between prime numbers and composite numbers universally, with reference to the mersenne odd numbers. That in a nutshell (forgive the pun) was how I derived the "algorithm" that I posted and was so enthusiastic about (without running it properly in SAGEMATH looking for things like false primes, etc, as I am still relatively inexperienced in Sagemath code). An interesting thing about the table was also, in addition to the "gridsieve" property of the mersenne numbers in ColM (as nalluded to earlier), I also thought the table/algorithm could be used to identify "twin primes" tweaking the relationship/algorithm slightly to say that when two consecutive row/column equivalent modulos for the algorithm is equal to the row/column number, then we potentially have a twin prime! , barring false positives of course :( That is it. That's how I came onto the relationship that I had posted. Last fiddled with by gophne on 20180102 at 02:21 Reason: spelling errors! Some info lost during cut & past 

20180102, 01:50  #150 
If I May
"Chris Halsall"
Sep 2002
Barbados
5×7×13×23 Posts 

20180102, 02:24  #151 
Feb 2017
3×5×11 Posts 

20180102, 02:27  #152 
If I May
"Chris Halsall"
Sep 2002
Barbados
10465_{10} Posts 

20180102, 02:29  #153  
Feb 2017
3·5·11 Posts 
Quote:


20180102, 02:32  #154 
Feb 2017
3·5·11 Posts 

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