30 Recap: If "3" doesn't divide evenly into an integer having "2" or "8" as a final digit, the decade that integer's in does not contain paired twin primes. [ Note: 0 through 9 is the first decade. ] Continuance: 15 45 75 105 135 165 195 225 255 285 - Have decided to try this with "3". 12/3 = 4, 18/3 = 6; 42/3 = 14, 48/3 = 16; 72/3 = 24, 78/3 = 26; so on. 5, 15, 25, 35, 45, 55, 65, 75, 85, 95. If one multiplies every 30 of these integers by "3", the chance of encountering paired twin primes is better but not absolute. Much of this has to do with the integer squares. 5, 35, 65, 95, and on, are the every 30. In the first instance, 9 is in the prior decade and 25 is in the following decade. In the second instance, 81 is two decades down and 121 is two decades up. In the third instance, 169 is three decades down and 225 is three decades up. However, in the fourth instance, 17 x 17 (289) or (16 x 18) + 1 or (8 x 36) + 1 is

inthe decade. Is there anything about the integers from 280 through 289 that signal this? 1 x 1 = 1, 3 x 3 = 9, 5 x 5 = 25, 7 x 7 = 49, 9 x 9 = 81 11 x 11 = 121, 13 x 13 = 169, 15 x 15 = 225, 17 x 17 = 289, 19 x 19 = 361 Pattern of final digits: 1, 9, 5, 9, 1 49 - 9 = 40 and 289 - 169 = 120. Beware that pown sqrt whose only or final digit is "3" or "7". Am heading higher to see what the spread is there. 21 x 21 = 441, 23 x 23 = 529, 25 x 25 = 625, 27 x 27 = 729, 29 x 29 = 841 169 - 49 = 120 and 529 - 289 = 240. Internally: 40, 120, 200. During lunch break, these: 1. The first paired twin primes occur in decade two; and, since every nine decades above that decade are the best initial places to look, decades 11, 20, 29, 38, 47, 56, 65, 74, 83, 92, and so on, are the ones.2. The following series of integers: 0 (0 x 1), 2 (1 x 2), 6 (2 x 3), 12 (3 x 4), 20 (4 x 5), 30 (5 x 6), 42 (6 x 7), 56 (7 x 8), 72 (8 x 9), 90 (9 x 10), 110 (10 x 11), and on.3. If one of these integers is multiplied by "4" and "1" is added to the product, the sum will equal an odd square. 72 x 4 = 288; 288 + 1 = 289. So 289 is an odd square, but of what?: 8 + 9. 4. 289 exists in the 29th decade. 5. Whatever decade is chosen, it is always wise to divide that decade's first integer by "4" and also to divide its ninth integer by "4" to see if the remainder is an integer which equals the product of two adjacent integers. Otherconsiderations: 2 x 0 = 0, 2 x 2 = 4, 2 x 4 = 8, 2 x 6 = 12, 2 x 8 = 16, 2 x 10 = 20, 2 x 12 = 24 2 x 6 = 4 x 3 2 x 10 = 4 x 5 2 x 36 = 4 x 18 = 8 x 9 = 72 - All the integers in the point 2 example are even integers. Their pattern is: 0 2 6 2 0 - In every decade where paired twin primes might be found, both that integer whose final digit is "2" and that integer whose final digit is "8" are evenly divisible by "6". - It might be that 288/6 = 48 is an indication 289 is a square since 49 is a square. - 1 + 8 = 9, 9 + 16 = 25, 25 + 24 = 49, 49 + 32 = 81, 81 + 40 = 121 9 - 3 = 6, 9 + 3 = 12; 25 - 5 = 20, 25 + 5 = 30; 49 - 7 = 42, 49 + 7 = 56 - #Brian A. J. Salchert

is a tiny wandering imaginary dinosaur which migrated from AOL in October of 2008.

## About Me

- brian (baj) salchert
- Rhodingeedaddee is my node blog. See
*my other blogs*and*recent posts*.

## Guide

[6-16-2009 Update Insert: Most of what is in this space is now moot. I found out what I was doing wrong and have reinstated Archives and Labels searches. They do work. However, in certain cases you may prefer Labels to Archives. Example: 1976 Today begins in November of 2006 and concludes in December of 2006, but there are other related posts in other months. Note: Labels only shows 20 posts at a time. There are 21 hubs, making 21 (which is for 1976 Today) an older hub.] ********************************* to my online poems and song lyrics using Archives. Use hubs for finding archival locations but do not link through them. Originally an AOL Journal, where the archive system was nothing like the system here, this blog was migrated from there to here in October of 2008. Today (Memorial/Veteran's Day, May 25, 2009) I discovered a glitch when trying to use a Blogger archive. Now, it may be template-related, but I am unable to return to S M or to the dashboard once I am in the Archives. Therefore, I've decided on this approach: a month-by-month post guide. The sw you see in the codes here stood for Salchert's Weblog when I began it in November of 2006. It later became Sprintedon Hollow. AOL provided what were called entry numbers, but they weren't consistent, and they didn't begin at the first cardinal number. That is why the numbers after "sw" came to be part of a post's code. ************** Here then is the month-by-month post guide: *2006* November: 00001 through 00046 - December: 00047 through 00056 -- *2007* January: 00057 through 00137 - February: 00138 through 00241 - March: 00242 through 00295 - April: 00296 through 00356 - May: 00357 through 00437 - June: 00438 through 00527 - July: 00528 though 00550 - August: 00551 through 00610 - September: 00611 through 00625 - October: 00626 through 00657 - November: 00658 through 00729 - December: 00730 through 00762 -- *2008* January: 00763 through 00791 - February: 00792 through 00826 - March: 00827 through 00849 - April: 00850 through 00872 - May: 00873 through 00907 - June: 00908 through 00931 - July: 00932 through 00955 - August: 00956 through 00993 - September 00994 through 01005 - October: 01006 through 01007 - November: 01008 through 01011 - December: 01012 through 01014 -- *2009* January: 01015 through 01021 - February: 01022 through 01028 - March: 01029 through 01033 - April: 01034 through 01036 - May: 01037 through 01044 - ******************************************************* 1976 Today: 2006/11 and 2006/12 -- Rooted Sky 2007: 2007/01/00063rsc -- Postures 2007: 2007/01/sw00137pc -- Sets: 2007/02/sw00215sgc -- Venturings: 2007/03/00216vc -- The Undulant Trees: 2007/03/00266utc -- This Day's Poem: 2007/03/00267tdpc -- Autobio: 2007/04/sw00316ac -- Fond du Lac: 2007/04/00339fdl -- Justan Tamarind: 2007/05/sw00366jtc -- Prayers in December: 2007/05/sw00393pindc -- June 2007: 2007/06/sw00440junec -- Seminary: 2007/07/sw00533semc -- Scatterings: 2008/08/00958sc ** Song Lyrics: 2008/02/sw00797slc ********** 2009-06-02: Have set S M to show 200 posts per page. Unfortunately, you will need to scroll to nearly the bottom of a page to get to the next older/newer page.

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## Sunday, May 11, 2008

### sw00884math--more-views-of-my-conjecture

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