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You are not logged in. #126 20130530 20:45:53
Re: My New Twin Prime NumbersHi Stangerzv, Last edited by phrontister (20130531 11:22:35) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #127 20130530 20:58:08
Re: My New Twin Prime NumbersOk, so far we got most of them but do you notice or not that digital root pair (1,4) occurs only once at Px=3 & Pt=3. By adding this digital root we get 1+4=5, yet the rest of digital roots above when added would give you a multiple of 3 digital roots examples, 1+2=3, 1+5=2x3, 1+8=3x3, 2+4=2x3, 2+7=3x3, 4+5=3x3, 5+7=12=>3, 7+8=15=2x3 but 1+7=8. I think it would be odd to get perfect prime pairs with the digital root {1,7} or if it does exist, it would be a special one. On the other hands, maybe there is only one pair of digital root of {1,4}. #128 20130530 23:10:05
Re: My New Twin Prime NumbersYes, it is interesting that all of the DR pairs I've got so far are a multiple of 3...except for that one case of {1,4} in Pₜ=3. There are a dozen or more solutions that I haven't posted, but they too are a multiple of 3. Last edited by phrontister (20130531 21:19:42) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #129 20130531 09:13:14
Re: My New Twin Prime Numbers
I think I'll give up on that idea, as the evaluations take faaaaar too long at the higher values and would take forever per result. Last edited by phrontister (20130531 21:19:11) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #130 20130531 11:30:07
Re: My New Twin Prime NumbersHi phrontister (1) and (2) (1)+(2), yields, Since Digital Root of is multiple of 3, so as with the digital roots of . Since none of the values of is multiple of 3 we can prove that Px is not a multiple of 3. Lets consider this equation, (1)(2) Taking digital root both sides yields If RHS is a negative DG, add 9. Since DG of RHS is never a multiple of 3 through prove by exhaustion. Therefore, digital root of LHS must also not a multiple of 3. Last edited by Stangerzv (20130531 12:07:44) #131 20130531 13:15:50
Re: My New Twin Prime NumbersHi Stangerzv, Last edited by phrontister (20130531 13:43:58) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #132 20130531 15:31:47
Re: My New Twin Prime NumbersHi phrontister It is becoming more interesting I guess. Last edited by Stangerzv (20130531 16:13:11) #133 20130531 18:04:25
Re: My New Twin Prime NumbersHi Stangerzv,
There are many cases with Pₓ<300,000 (that's all I've tested to) where DR=3 for Pₜ=2. Last edited by phrontister (20130601 20:28:35) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #134 20130531 20:16:43
Re: My New Twin Prime NumbersSo, it means the sums of prime power for prime would be a multiple of 3 then. But have you tried prime power bigger than 2? I think there is no digital root of 3 for power greater than 2. #135 20130531 20:55:44
Re: My New Twin Prime Numbers
Yes, I had tried powers higher than 2, but not many. I found these: Pₜ=5 Last edited by phrontister (20130531 21:17:45) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #136 20130531 21:06:09
Re: My New Twin Prime NumbersOk, 2 and 3 always behave that way. I missed Pt=3 but I think more than Pt=3 the DG=3 would diminish unless you can find a counter example. #137 20130531 21:15:55
Re: My New Twin Prime NumbersSorry, my edit to post #135 crossed with your latest post. I had added a DR=3 for Pₜ=5. Last edited by phrontister (20130531 21:29:24) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #138 20130531 21:41:41
Re: My New Twin Prime NumbersSo, it seems that the sums of primepower would be a multiple of 3. Well, do you think is it possible for it to have other than multiple of 3? for Pt>3. Maybe I need to learn programming again and run it on my computer. Mine is just core i5. Maybe it is just enough for smaller numbers Anyway, phrontister, thanks for the input, it is really a big help. #139 20130531 22:18:41
Re: My New Twin Prime Numbers
Yes, that would be highly likely, other than for the first (smallest) result of Pₜ=3.
I lack experience and knowledge and can't think of any way of proving that it is not possible, but from the fact that I've tested quite a few Pₜ and all of them other than the first solution for Pₜ=3 resulted in DR=a multiple of 3, it certainly seems very improbable.
I don't know how yours compares with mine, which is an AMD Athlon Dual Core 5200+ 2.71GHz with 3Gb RAM, but larger Pₜ certainly slow things down for mine. "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #140 20130601 19:12:16
Re: My New Twin Prime NumbersIt is easier to put something than making sure it is true for all. I think it would take like forever to proof that, why these prime always working with 3, 6 & 9 through computation. #141 20130601 20:16:25
Re: My New Twin Prime Numbers
It might even take longer than forever(!), as the way we're doing it means we can only ever test a tiny sample from an infinite range. I guess a conclusive proof would have to be by algebraic logic or some other means of argument that I wouldn't have any idea about as my maths level is too low. Someone else with more knowledge would have a better idea about how to construct a proof...or know whether or not it's even feasible.
I'm not sure I understand you correctly. Last edited by phrontister (20130601 20:50:47) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #142 20130602 04:59:31
Re: My New Twin Prime NumbersWell, DR for even number not always an even but also can be a prime or odd number. DR(12)=3. What did I mean is that, would sums of primepower with digital root 3, 6 and 9 always resulting in a prime Ps when Px also a prime? This is because, I think there are not that many of sums of primepower with digital root 3, 6 & 9 could exist at the same time with prime Px, if they do, would all of them resulted in prime Ps or not necessarily to be prime. Last edited by Stangerzv (20130602 05:06:57) #143 20130603 13:12:31
Re: My New Twin Prime Numbers
Sorry, I'd overlooked the fact that "+/" (ie, +Px and Px) isn't included this time, otherwise Ps would have to be even for Ps+Px and PsPx to be prime.
I can only find even numbers for Ps with DR=3, 6 or 9 when Px is prime.
It's not that I actually feel bad about it. I enjoy doing puzzles and I know enough to be able to solve a reasonable range of them with logic, pen and paper, my calculator, Excel, Mathematica and BASIC programming. That keeps me pretty happy, but sometimes I wish I had more knowledge so that I could understand more of the posts here on MIF. I don't have the desire, dedication or time to broaden my maths knowledge much, but have been picking up a few things here and there from bobbym and others. Last edited by phrontister (20130603 18:21:23) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #144 20130605 10:49:06
Re: My New Twin Prime NumbersHere's a table like the one in my previous post, but this one also includes Ps and the range of Pt. "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #145 20130606 00:30:12
Re: My New Twin Prime NumbersHi phrontister, thanks for the input. It would be wonderful to have a supercomputer indeed. I used to work with OSCAR CraySGI supercomputer when I was in the UK last time. I wish I was doing mathematics those times and the calculation would be lightening speed fast for sure. It is a sure thing that next Ps would be a rare thing and finding the bigger one is something kool because the probability to get the twin prime at higher Px is very small. It would be more challenging than finding Mersenne's prime because these primes exist in pair and usually bigger primes more than few millions digits rarely occurred next to each other. #146 20131021 02:02:15
Re: My New Twin Prime NumbersDear Bobbym and Phrontister #147 20131021 02:25:21
Re: My New Twin Prime NumbersHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #148 20131021 20:49:45
Re: My New Twin Prime NumbersHi Stangerzv, Last edited by phrontister (20131021 21:24:11) "The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do."  Ted Nelson #149 20131022 00:03:24
Re: My New Twin Prime NumbersBobbym & Phrontister. Thanks, I would mention this forum then:) #150 20131022 00:28:19
Re: My New Twin Prime Numbers
Oh boy, if only some of that were true. My cousin is being kind. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 