Hi Dave! Suzanne ask that I write and initiate you into the ancient and honorable mysteries of the properties of prime numbers - or their reciprocals, to be precise! Compared to pi which goes on forever without repeating itself, the reciprocals of primes repeat themselves infinitely, with some interesting characteristics. as an example, the value of 1/17 = .058823529411764705882352941176470588235294 . . . . . . When you look at the series, you see that the repeat begins after 1176470. The number of integers before the repeat is 17. In order to amaze your friends and many math majors (my brother-in-law was a math professor at Stanford and didnt know this) all you need to do is memorize the 17 digits beginning with 5 and ending with 0: 5882352941176470 Now if you ask your subject to write this number down (present it as a random number you just made up) and to multiply it by any number up to 17, the answer will be the exact same number - it will just start at a different spot in the sequence. To figure out where it will start, mentally multiply the number chosen by 6. (the first 2 numbers in the series are 58 (think of it as 5.8 - which is slightly less than 6). For example, if the number chosen is 9, 6 x 9 = 54. Now you go through the series in your head and find the sequence of two number which is slightly under 54. In this case the 6th and 7th numbers in the series are 52. Therefore the answer to: what do you get when you multiply 9 x 5882352941176470 is: 52941176470588230 [ the zero on the end you simply have to remember to add on since the sequence ends in zero ] If you want to multiply the number by 13, then 13 x 6 = 78 so you look for the 2 integers in the series that are the nearest (but below) 78. In this case 76. Therefore 13 x 5882352941176470 is: 76470588235294110 The same characteristic applies to the reciprocals of all primes, so if you wish to memorize the reciprocal of 4493, it will be 4493 digits long and you will be able to perform stupendous feats of mathematical prestidigitation, however I always found it was hard to hold an audience for this recitation so I limit myself to 17 digits. . . . I also noticed that if you take the numbers in the series and start on the right side and add each to its neighbor the final result is the same sequence starting with 6470588235294117. What this has to do with anything is beyond me, but its my contribution to the cosmological body of mathematical knowledge. The one other value of the series, is that once imprinted in your brain it forms the basis for short series of numbers to use at will for things like passwords, hotel safes, and all matter of useful applications. If you are so inclined. Having told you this you must now be sworn to secrecy, and having achieved this level of enlightenment Im sure you will be much happier in your future endeavors. If you have any lingering questions about these mystical phenomenon Suzanne will be hay to clear them up as long as the number 4 is not involved. Dick Jeffries
Posted on: Fri, 02 Jan 2015 22:20:38 +0000