29 Yesterday (Friday, May 09, 2008) I concluded my sw00882math/ descension-by-squares-groups/2841 with this conjecture: Regarding paired twin primes, the even integer between one of the twin primes is always divisible by "4" and the even integer between the other of the twin primes is always divisible by "6". Why did I posit this seemingly senseless conjecture? Because I wanted to use even integers since I had set up a descension-by-squares grouping controlled by "4". As it happens, the only way my groupings matter is that it was through them that I uncovered the "4" and "6" phenomenon. Early this after- noon, I was trying to find out if I was wrong, an effort which led to: "3" divides into every six integers, the final digits of which (excluding the special case: 3 x 3) are 5, 1, 7, 3, 9 as in 15, 21, 27, 33, 39. Here is a run with the above numbers in italics: 11 13

1517 192123 252729 313335 373941 43 If the final digit is "1" or "7" or "3" or "9", there cannot be any paired twins primes because 1 + 4 = 5, 7 - 2 = 5, 3 + 2 = 5, 9 - 4 = 5. Therefore, the final digit must be "5" and the integer must be divisible by "3". 5 - 3 = 2 and 5 + 3 = 8. This then is my proof, such as it is. Also, where the integer whose final digit is "5" is not divisible by "3"/ neither the integer whose final digit is "2" nor the integer whose final digit is "8" is evenly divisible by "6". My effort began with this: 6102108 114 120 126 132 4 100 104108112 116 120 124 128 132 136 - - - 99 101 103 105 107 109 111 113 115 117 119 121 123 125 127 3 3x5x7 3 5 3 7 11 3 5 5:01 PM - Have uncovered a flaw. At the early going it involves "7". It is quite obvious, but I failed to check. "3" divides evenly into an integer whose final digit is "5" every thirty integers greater than "15" but it isn't until ninety above "15" that paired twin primes are encountered. [ This doesn't invalidate my conjecture as stated, but it certainly weakens it. ] One obstacle is the odd square. However, the (8 x an nnss term) + 1 method isn't the only way to find an odd square. These mulitplications: 2 x 4, 4 x 6, 6 x 8, 8 x 10, 10 x 20, and so on + 1 is another method. But I had mentioned "7". Every fourteen from forty-nine it's out to clip ya, and it doesn't follow an easy-to-detect routine the way "5" and "3" do. Perhaps "3" can help, or "5", or both. Some integers "7" divides evenly into: one above 55, two below 65, two above 75, one below 85, one above 90, two below 100, at 105, two above 110, one below 120, one above 125, two below 135, at 140, two above 145. Dizzy yet? Which one did I miss? Correct: at 70. Routine? Going back to 7 x 1, the routine begins at two above. So: two above, one below, one above, two below, at | two above, one below, one above, two below, at. I hate "7", which is to say nothing about the greater more difficult integers. What about how it relates to mulitiples of "3"? Which ones? How about just those that add to 3. four above 3, two above 12, at 21, two below 30, four below 39, three above 39, one above 48, one below 57, three below 66 | four above 66, two above 75, at 84, two below 93, four below 102, three above 102, one above 111, one below 120, three below 129. All this reminds of a poem I wrote in 2006. After I find it I'll place a link to it. It is 9:35 PM. Earlier a storm passed. Need to see if another one's coming. Gusts just thrust us. Satellite's showing an enlarging green patch over this city. Dost one blame it on the coal- fired power plant? Or is it merely a reflection of the city's lights? "Bone Ache" is the poem. It is the fourth one on its page. A quick six lines. It was written September 29, 2006. It fits this occasion. #Brian A. J. Salchert

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

## About Me

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## 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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## Saturday, May 10, 2008

### sw00883math--my-paired-twin-primes-conjecture

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