... Phil, p is a prime congruent to +/- 1 mod 8. My question now is, "Is the order of 2 mod p equal to (p-1)/2? I think so, but have no proof.... The...
8487
Phil Carmody
thefatphil
Aug 29, 2002 9:49 pm
... Seconded. Pavlos, quite simply, this is a _brilliant_ discovery, and I take my hat off to you. It's definitely worth more investigation, thanks for sharing...
8488
Ignacio Larrosa Ca...
ilarrosa
Aug 29, 2002 9:50 pm
... From: "Jon Perry" <perry@...> To: <primenumbers@yahoogroups.com> Sent: Thursday, August 29, 2002 7:32 PM Subject: RE: [PrimeNumbers] Something...
8489
jbrennen
Aug 29, 2002 9:51 pm
... Actually, Phil's examples are exactly relevant to the question you asked. If p==31, the order of 2 mod p is 5, which divides 15 == (p-1)/2. If p==73, the...
8490
Phil Carmody
thefatphil
Aug 29, 2002 9:56 pm
... Tabulate the values of O2(p) (the order of 2 mod p), and (p-1)/2 for p in {31, 73, 89, 127, 113, 151 } I'll give you a clue - the first two entries is P :...
8491
Phil Carmody
thefatphil
Aug 29, 2002 10:00 pm
... Amusingly enough the ability for the odd numbers or the prime to be negative is ambiguous. Strictly, the negative primes are prime, but are not normally ...
8492
David Cleaver
wraithx@...
Aug 30, 2002 2:14 am
... Wow! I ran your program on my P-IV 1.8GHz machine and it took 100 seconds to run up to the 10^7 limit. How many P-II/350's you runnin?!? Anyway, I...
8493
Pavlos N
pavlos199@...
Aug 30, 2002 8:00 am
I finally was able to prove that no finite covering set exists,that is,there are infinitely many primes that divide k*2^n+1 for the specific k's as n ...
8494
Pavlos N
pavlos199@...
Aug 30, 2002 8:00 am
I finally was able to prove that no finite covering set exists,that is,there are infinitely many primes that divide k*2^n+1 for the specific k's as n ...
8495
Phil Carmody
thefatphil
Aug 30, 2002 8:33 am
... It seems that the proof of having a non-finite covering set for the original composite sierpinski form is mapped into either a proof of a non-finite ...
8496
Ignacio Larrosa Ca...
ilarrosa
Aug 30, 2002 11:07 am
In http://www.cwi.nl/~walter/papers/LL92.ps.gz, seems its say that no other < 10^9. Althought my Dutch is very much worst that my English ... :(( Saludos, ...
8497
Phil Carmody
thefatphil
Aug 30, 2002 11:11 am
... [Brough back on list] Indeed - It's Pavlos' baby, and he should certainly put it on as many tables as possible. If I don't see it reach sci.math...
8498
Phil Carmody
thefatphil
Aug 30, 2002 11:20 am
... Note that "there are infinitely many primes that divide k*2^n+1 for the specific k's as n varies" is _not_ the equivalent of there being no finite covering...
8499
Max B
zen_ghost_floating@...
Aug 30, 2002 12:35 pm
... I was only aware of the 5777 counterexample and tossed out "5" arbitrarily. Thanks to everyone who responded to this!...
8500
jbrennen
Aug 30, 2002 2:37 pm
Note that there is a subset of Pavlos' numbers which do in fact have a finite covering set, and that this subset has positive density. The following covering...
8501
Phil Carmody
thefatphil
Aug 30, 2002 6:05 pm
... I can't find a number below 10^9 that requires a prime greater than 29089961. I think 2e9 can be reached with primes <= 46376861 Ditto 3e9 with primes to...
8502
Ignacio Larrosa Ca...
ilarrosa
Aug 30, 2002 6:25 pm
... From: "Phil Carmody" <thefatphil@...> To: "primenumbers" <primenumbers@yahoogroups.com> Sent: Friday, August 30, 2002 8:05 PM Subject: Re:...
8503
Jon Perry
jon_perryuk
Aug 30, 2002 7:12 pm
... These days 'sufficiently large' shouldn't count as a proof - a proof should only be considered complete iff computations can carry the work load up to the...
8504
Jon Perry
jon_perryuk
Aug 30, 2002 7:14 pm
Amusingly enough the ability for the odd numbers or the prime to be negative is ambiguous. Strictly, the negative primes are prime, but are not normally ...
8505
Jack Brennen
jbrennen
Aug 30, 2002 7:23 pm
... No, Jon, Goldbach's other conjecture... The one we've been discussing in this thread... About the form p+2*a^2... Allowing negative numbers would be...
8506
Phil Carmody
thefatphil
Aug 30, 2002 11:52 pm
... And while I was listening to an amazing Anthrax cover-band this evening, I came up with a small idea for an optimisation, so I'll code that and then go to...
8507
djbroadhurst
Aug 31, 2002 3:53 pm
Just looked in between trips. Skipping predictable Brown trash, I saw a really _neat_ thing by Pavlos Saridis: To make N=k*2^n+1 always composite [Saridis]: a)...
8508
Ignacio Larrosa Ca...
ilarrosa
Aug 31, 2002 4:25 pm
... From: "Phil Carmody" <thefatphil@...> To: "primenumbers" <primenumbers@yahoogroups.com> Sent: Saturday, August 31, 2002 1:52 AM Subject: Re:...
8509
Phil Carmody
thefatphil
Aug 31, 2002 8:58 pm
... I just threw something together in an ad hoc fashion yesterday. It's truly horrid code, and I'm quite embarassed about it, it's 'write-only code'. It only...
8510
djbroadhurst
Aug 31, 2002 9:02 pm
Thanks for those Goodstein pointers, Matt. Is there any non-trivial example where it is known precisely how many steps one takes to get to zero? If so, would...
8511
Sebastian Martin
sebi_sebi
Aug 31, 2002 9:43 pm
Hello all: you can see my article about prime numbers at: http://www.gallup.unm.edu/~Smarandache/SMRuiz-nextprime.pdf and other formulas at: ...
8512
Phil Carmody
thefatphil
Aug 31, 2002 9:55 pm
... What computatioal complexity do algorithms based on your formulae have? For example, what's the point in replacing the sigma0 function with a sum that has...
8513
Sebastian Martin
sebi_sebi
Aug 31, 2002 10:19 pm
The computational complexity is (nlogn)^3 for the problem 38 formulas, I have not studied the complexity for the problem 39. And the formulas in the article...
8514
Phil Carmody
thefatphil
Sep 1, 2002 12:19 am
... It depends on how you judge the size of the problem, I should have been more explicit. It's fairly common to view the size of a problem parametrised by the...
8515
Sebastian Martin
sebi_sebi
Sep 1, 2002 12:44 am
I already know that the topic doesn't have a lot of practical interest. But I hope this can have certain theoretical interest. This perhaps could help somebody...
