This morning the first known AP25 has been discovered: 6171054912832631 + 366384*23#*n, for n=0 to 24 (Raanan Chermoni & Jaroslaw Wroblewski, May 17 2008) My...
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Phil Carmody
thefatphil
May 17, 2008 8:47 am
... Wow! A marvelous find. I think a lot of people here have been crossing their fingers for you over the last few months as the AP24s have been coming in, I...
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jarek372000
May 17, 2008 9:45 am
I am not sure what was the exact CPU power used, as Raanan was distributing the program among his computers, and also the number and kind of computers he had...
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Paul Schmidt
pschmid0
May 17, 2008 1:33 pm
Jarek, I might be interested in helping to set up a distributed system. Since each segment is independent, this shouldn't take anything fancy. I am a...
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Jens Kruse Andersen
jkand71
May 17, 2008 4:30 pm
... Huge congratulations! This is a very impressive and well deserved feat. http://hjem.get2net.dk/jka/math/aprecords.htm is updated. As the only known AP25 it...
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Lélio Ribeiro de P...
lelio_73
May 17, 2008 4:58 pm
Each Sierpinski (and Riesel) number and the dual of it always have the same covering set as it is easy to see. So we only need to find a prime for a candidate...
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Chris Caldwell
primemogul
May 17, 2008 6:40 pm
... I agree! Decided to change my 2006 banner notes about the last Mersenne to this AP on my "main" page primes.utm.edu/ and primes.utm.edu/largest.html ... ...
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Jens Kruse Andersen
jkand71
May 17, 2008 8:47 pm
... Nice. I see it's already in Prime Curios!: http://primes.utm.edu/curios/page.php/6171054912832631.html This can also be updated: ...
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Phil Carmody
thefatphil
May 18, 2008 8:04 am
From: Lélio Ribeiro de Paula ... By Sierpinski's definitions, finding a prime in the dual set does not remove the k value as a candidate to be what was later...
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Jack Brennen
jbrennen
May 18, 2008 2:42 pm
... Indeed, the prime of the form k+2^n might be in the covering set for the numbers of the form k*2^n+1....
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julienbenney
May 19, 2008 2:11 am
Your idea is very interesting. My readings about near-repdigit numbers has made me fascinated by Sierpinski and Riesel numbers and especially their covering...
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Lélio Ribeiro de P...
lelio_73
May 19, 2008 10:50 am
... No, it cannot. The covering sets of all known Riesel and Sierpinski numbers are exactly the same as that of their duals, as can be easily seen. So if a...
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Phil Carmody
thefatphil
May 19, 2008 10:59 am
... Now reread what Jack wrote (which was also going be in my original post too, but thinking that it was a bit obvious I removed it for brevity), and think a...
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Jack Brennen
jbrennen
May 19, 2008 2:39 pm
... I tried (in private email) giving the example of the dual sequences: 10^n-7 7*10^n-1 They both have the same covering set (it can be found in under a ...
19371
jarek372000
May 21, 2008 9:47 am
I have prepared the first version of the description of the algorithm I have used for the AP24 search (and which was used on Raanan's computers for the AP25...
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Mohd Salleh
nimzo_indy
May 22, 2008 12:48 am
Come & join this today.. You can get up to usd10000.00 per month.. What are you waiting for? Click here to view video presentation ->...
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aldrich617
May 23, 2008 3:49 am
Formulas for producing chains of primes may be derived from known examples. If you have a quadratic equation that already has a notable chain , such as 10x^2...
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jarek372000
May 23, 2008 8:20 am
I have found the following AP19 2027663243 + 1002606*19#*n, n=0..18 which, I believe, improves 24 years old "minimal known start AP19" record. The total CPU...
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Jens Kruse Andersen
jkand71
May 23, 2008 11:22 am
... Congrats. The record table at http://hjem.get2net.dk/jka/math/aprecords.htm#minimalstart is updated. The old record was 8297644387 + 431*19#*n, n=0..18,...
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marcus.michel
May 23, 2008 3:33 pm
In http://www.upforthecount.com/math/mandrill.html, Walter Nissen has defined a primitive friendly pair (pfp): 1. Abundancy is defined as the ratio of the...
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Kermit Rose
kermit1941
May 24, 2008 3:25 am
(1) [ Definition ] A positive integer p is prime if and only if a > 0 divides p implies a = 1 or a = p. (2) A positive integer p is prime if and only if p...
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Roger L. Bagula
rlbagulatftn
May 24, 2008 9:38 am
I actually didn't find "bad primes" defined in any number theory way... they were associated with a Calabi-Yau based L-function in a paper with no real good...
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marcus.michel
May 24, 2008 3:10 pm
The dpfp with the highest abundancy that I have found is 5^3*7^3*11*13^2*17*43*61^2*67*71*79*97*461^3*1279*106261 ...
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marcus.michel
May 24, 2008 3:13 pm
A single dpfp is known with the same primes for both members 3^5*11*13^2 3^4*11^3*13 abundancy 6832/3861 Is it possible to find other deficient pairs with the...
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marcus.michel
May 24, 2008 4:03 pm
Some dpfps have the property that both members start with the same prime. Here are same instances: 2^3*19^2*127 2*7^2*13*19^3*181 abundancy 720/361 3^3*5 ...
19382
aldrich617
May 25, 2008 1:28 pm
Well, got the official word from D.B.: linear transforms are of no value and egregious factors are annoying. But then again he says that about almost...
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Paul Underwood
paulunderwooduk
May 25, 2008 2:49 pm
... When "X" is odd the expressions are even. They are not equal to 2, so they are then composite. ... ? factor(x^4-97*x^3+3294*x^2-45458*x+213589) [x^4 -...
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jarek372000
May 26, 2008 4:09 am
Here are a few things I have done about 2nd kind Cunningham Chains. 1. I have determined that the known solution 3203000719597029781 is the only start of a 2nd...
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Kermit Rose
kermit1941
May 26, 2008 4:33 am
1a. Quadratic Prime Chains Posted by: "aldrich617" aldrich617@... aldrich617 Date: Sun May 25, 2008 6:28 am ((PDT)) Can anyone factor X4 - 97X3 + 3294X2...
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Jens Kruse Andersen
jkand71
May 26, 2008 11:05 am
... Congratulations! If you use just some of the cpu power from AP hunting on Cunningham chains then I guess you could dominate the record tables. ...
