... Did you look at the first link I gave you: http://www.fermatquotient.com/FermatQuotienten/FermQ_Sort It includes those bases searched to 5.074*10^12 (with...
18977
Mark Rodenkirch
mgrogue
Jun 1, 2007 6:52 pm
This was meant to be sent to the group and I sent it to Jens by accident. If anyone else here has a PowerPC G5, I have a program that could search a range of...
18978
Kevin Acres
codefinda
Jun 1, 2007 9:45 pm
I did indeed look through all of the interesting links that you sent. I'm just wondering if I can get the time to work through the information and see if it...
18979
terranorca
Jun 2, 2007 12:13 am
Mathematicians studying prime numbers have remarked on the duality of their behavior. For example, Andrew Odlyzko in his 2006 IRMACS lecture, states that "even...
18980
Joshua Zucker
zucker
Jun 2, 2007 7:27 am
I think the randomness and bell curve are in one sense much more predictable than primes: if you flip a coin long enough, you are eventually going to get N ...
18981
elevensmooth
Jun 3, 2007 4:43 am
... I suspect it's provable, but I can't locate my copy of Hardy and Wright tonight to skim for inspiration. The minimal value is the column called "order" at ...
18982
Phil Carmody
thefatphil
Jun 3, 2007 2:21 pm
... Subscirbe! Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed [stolen with...
18983
Mark Rodenkirch
mgrogue
Jun 3, 2007 7:47 pm
... YGM. --Mark [Non-text portions of this message have been removed]...
18984
Tom
thoeng
Jun 3, 2007 10:28 pm
The months of April and May have proved very productive with more than 2200 widths with denser packings (some widths with 4 additional primes) The slope of the...
18985
Phil Carmody
thefatphil
Jun 4, 2007 1:13 pm
... As always, Tom, thanks for keeping us updated. I'm glad that you're having so much success with such hunts. It's one of the things that I never quite got...
18986
Mark Underwood
marku606
Jun 4, 2007 3:29 pm
I was having some fun putting (rather arbitrary!) restrictions on the goldbach conjecture to make it come *close* to failing. (Goldbach conjecture: Every even...
18987
mistermac39
Jun 5, 2007 3:17 am
Of course if one of your "close" to failing cases is the first of a prime number pair, your next even number will be a close or better success. A real failure...
18988
Shi Huang
shuangtheman
Jun 5, 2007 8:17 am
Mathematics is linked with determinism and predictability. Thus the seeming randomness of primes is striking. The duality is what makes the primes so ...
18989
elevensmooth
Jun 5, 2007 2:54 pm
... Yes. Let d be the smallest value so that p divides b^d-1. First observe that if b^x-1 and b^y-1 and both divisible by p^2 (or any other number), then...
18990
Wes
thepaigetobe...
Jun 7, 2007 3:17 am
I was reading where if Merten's sum of Moebius terms could be shown to be big O of k^(1/2+epsilon) that it proves the Riemman hypothesis. I was looking at the...
18991
Alec Smart
pvp4tw
Jun 8, 2007 8:09 am
I was doing some thinking the other day, and ran into some neat stuff: What percentage of all integers are even, or divisible by 2? At first, I thought it...
18992
Phil Carmody
thefatphil
Jun 8, 2007 8:36 am
... Research "Natural Density". The limsup and liminf converge to 50%, so it's 50%. Quite why you don't think the density on the sets {0,1} and {0,1,2,3}, ......
18993
Alec Smart
pvp4tw
Jun 8, 2007 10:24 am
Thanks! Much appreciated, really interesting stuff. ... Boardwalk for $500? In 2007? Ha! Play Monopoly Here and Now (it's updated for today's economy) at...
18994
Jens Kruse Andersen
jkand71
Jun 8, 2007 1:37 pm
... I'm not sure what you mean by "solely divisible by that number alone". Phil guessed you meant least prime factor (lpf). I also guess that, but then your...
18995
Phil Carmody
thefatphil
Jun 8, 2007 2:53 pm
... I didn't spot that, and tacitly, but incorrectly, supported them. Yours are of course correct. Phil () ASCII ribbon campaign () Hopeless ribbon...
18996
Alec Smart
pvp4tw
Jun 8, 2007 10:34 pm
Ahh, good catch. Yeah, my numbers were off... I'm kind of interested in what the graphs look like, because I've never encountered another series of numbers...
18997
Mark Underwood
marku606
Jun 9, 2007 12:40 pm
... primes.) ... It turns out that for GP Pari to work on my mac, I needed to get a C compiler which will produce programs which could run on the mac. Apple ...
18998
Alec Smart
pvp4tw
Jun 10, 2007 6:17 am
Actually, I was wondering if there was a way to predict the lines without knowing the primes in question... an approximation, at the very least. I was thinking...
18999
Alan Eliasen
aeliasen
Jun 11, 2007 1:02 am
... You'll probably note, if you follow the discussions in this group, that a large number of participants use the free PARI/GP package for number theory...
19000
Kevin
codefinda
Jun 12, 2007 4:41 am
I'm trying to factor the last part of 2^1896-1 or: 72009645598802661741572237135153453757864421072572019369424603012486080 ...
19001
Kevin Acres
codefinda
Jun 12, 2007 6:16 am
Sorry, Forget that, I hadn't checked for divisibility by 1896 before I posted. Which is what comes of too much haste and not enough speed. Kevin. ... I'm...
19002
elevensmooth
Jun 12, 2007 1:06 pm
... Do you just want the factors, or do you want to learn how to find the factors? If you just want the factors, you can use Alpertron at ...
19003
Søren Nielsen
srentospace
Jun 12, 2007 3:16 pm
in these case to substitute....
19004
Kevin Acres
codefinda
Jun 12, 2007 10:46 pm
... From: elevensmooth [mailto:elevensmooth@...] Sent: 12 June 2007 22:57 To: primenumbers@yahoogroups.com Subject: [PrimeNumbers] Re: Naive question on...
19005
N.L.
nluhn
Jun 13, 2007 5:09 pm
Hello, I have found in few seconds with my program: 2^1896 have prime factor 201487636602438195784363 I don't know, this factor are known ? regards ...
