... This page mentions the incompatibility of the 2 conjectures here http://en.wikipedia.org/wiki/Second_Hardy-Littlewood_conjecture and references your...
19080
jtrjtrjtr2001
Sep 9, 2007 4:41 am
Hi, Let p2 be a large prime. We find another large random prime p1, such that y = (2*p1*p2) + 1. Is there any way, one could quantify the probability of y...
19081
Phil Carmody
thefatphil
Sep 9, 2007 9:38 am
... Well, it's just like any arbitrary number of the same size except that it's even, it's not divisible by p1, and it's not divisible by p2. Therefore there's...
19082
Dirk Augustin
trex400
Sep 11, 2007 6:29 pm
Hello group, after about 140 days on an Athlon XP 2600 with the use of a combined sieving and prp program written by Jens Kruse Andersen, I found a new ...
19083
Christ van Willegen
cvwillegen
Sep 12, 2007 6:27 am
... Congratulations on your new record! Christ van Willegen -- 09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0...
19084
odj17497
Sep 13, 2007 3:02 pm
To all interested: Sometimes there's a multiple of 210 that's symmetrically surrounded by twelve primes, six on both sides, by distances of 1, 11, 13, 17, 19,...
19085
Bill Bouris
leavemsg1
Sep 13, 2007 8:26 pm
Group,... know that this is a modest effort to explain why only so few Fermat numbers are 'prime'. Overview: It can be shown that F(1)...F(4) are the only...
19086
Jack Brennen
jbrennen
Sep 14, 2007 12:37 pm
... And y is not congruent to 1 mod 3, or to 1 mod 5, or to 1 mod 7, etc. Which should make y somewhat more likely to be divisible by these small numbers......
19087
Jens Kruse Andersen
jkand71
Sep 14, 2007 12:37 pm
... Phil meant y is odd, but another factor must also be considered. If q is a random odd prime other than p1 and p2, then q does not divide y-1. q must divide...
19088
Phil Carmody
thefatphil
Sep 14, 2007 1:28 pm
... Good catch, Jack! Phil () ASCII ribbon campaign () Hopeless ribbon campaign /\ against HTML mail /\ against gratuitous bloodshed ...
19089
Johannes Z.
joz1977
Sep 14, 2007 1:42 pm
Hi Gerald, I m not a mathguy, but i would like to show you a different approach, which brings up rather similar findings regarding to multiples of 210, ...
19090
Jens Kruse Andersen
jkand71
Sep 14, 2007 3:14 pm
... All 4 above posts were mailed September 9 but it took 5 days to deliver the posts by Jack and I. We are far apart and the posts showed up the same minute...
19091
Bill Bouris
leavemsg1
Sep 16, 2007 4:57 pm
edited from earlier e-mail... no comments? the 'pair-wise effort has to be continuous to produce more Fer-mat primes. ... should say... has been once removed,...
19092
Kermit Rose
kermit1941
Sep 22, 2007 4:19 am
I'm making progress, but I know I'm not yet at the frontier of factoring capability. Here is an example of my current program output. The coefficients of the...
19093
w_sindelar@...
Sep 24, 2007 1:07 pm
The only pertinent web reference I could find is Green and Tao's theorem which says that for every integer k=1 or greater, one can find an arithmetic...
19094
Jens Kruse Andersen
jkand71
Sep 25, 2007 3:16 am
... This follows from the widely believed conjecture that all admissible prime constellations have infinitely many occurrences. If the conjecture is true then...
19095
Bill Bouris
leavemsg1
Sep 25, 2007 1:28 pm
Group, Q: Why are the number of them... finite? A: They are bounded by two 'modulo' conditions, namely... G(x): 2^(2^(x+1)) +1 == 2^q (mod (2^x +1)) H(x):...
19096
w_sindelar@...
Sep 26, 2007 7:48 pm
Thank you once again, Jens. I value your responses. I would like to add a few comments in reply. ... I'm lost here. Seems like a convoluted approach. Here's...
19097
Jens Kruse Andersen
jkand71
Sep 27, 2007 12:01 am
... You asked for comments on your statement (which is an unproven guess). I briefly showed that it would follow from a well-known and trusted conjecture,...
19098
Bill Bouris
leavemsg1
Sep 27, 2007 12:55 am
Group, I believe that (O)dd (P)erfect (N)umbers do NOT exist in the same manner as (E)ven (P)erfect (N)umbers do! If we allow the generic formula of...
19099
elevensmooth
Sep 27, 2007 1:55 am
... I'll try. Are you aware of the concept of "admissible constellations?" For example, twin primes, x and x+2, are believed to occur infinitely often. A...
19100
elevensmooth
Sep 27, 2007 2:10 am
Bill, Your analysis appears to be restricted to consideration of odd perfect numbers with only two distinct prime divisors. It's known that any odd perfect...
19101
Kermit Rose
kermit1941
Sep 28, 2007 12:38 am
An odd perfect number, N, would have to be of the form N = p1^a1 p2^a2 . . . p_k^a_k where each of the p's are odd primes. The sum of the divisors of N,...
19102
w_sindelar@...
Sep 29, 2007 1:20 pm
... Jens, I think I may have offended you by writing "I'm lost here. Seems like a convoluted approach." Looking back at this, I can see that it can be taken as...
19103
w_sindelar@...
Sep 29, 2007 1:20 pm
On Thu, 27 Sep 2007 01:55:00 -0000 "elevensmooth" ... I'm glad you did, and I thank you. You must be a mind reader. You somehow sensed why I got lost trying to...
19104
w_sindelar@...
Sep 29, 2007 1:25 pm
... Jens, I think I may have offended you by writing "I'm lost here. Seems like a convoluted approach." Looking back at this, I can see that it can be taken as...
19105
w_sindelar@...
Sep 29, 2007 1:25 pm
On Thu, 27 Sep 2007 01:55:00 -0000 "elevensmooth" ... I'm glad you did, and I thank you. You must be a mind reader. You somehow sensed why I got lost trying to...
19106
Jens Kruse Andersen
jkand71
Sep 30, 2007 12:40 am
... No problem. You can search more information about admissible constellations with a search engine. If a prime p <= k does not divide the common difference...
19107
leavemsg1
Sep 30, 2007 4:20 pm
I am not satisfied that Li(x) describes the number of primes < x I have a new calculation that gives... x= 1000 Ki(1000)= 167.9 and... x= 7919 Ki(7919)=...
19108
Andrey Kulsha
andrey_601
Sep 30, 2007 7:52 pm
... http://en.wikipedia.org/w/index.php?title=Prime-counting_function#Formulas_for_prime-counting_functions See the paragraph about the Riemann's R-function. ...
