Marty, ... So far, we're in agreement. ... Actually, it might be you not realizing that Lelio most likely made a typo and wrote "30 +/- 1" instead of "30n +/-...
21685
Alberto Zelaya
albrtzlya
Aug 1, 2010 3:53 pm
Anexed to this email I m sending TWINS FOR KIDS an essay that was intended to demonstrate that there is a discernible pattern of distribution of twin primes...
21686
Chris Caldwell
primemogul
Aug 3, 2010 5:03 am
From: Jens Franke Sent: Thursday, July 29, 2010 2:47 PM Subject: pi(10^24) Using an analytic method assuming (for the current calculation) the Riemann...
21687
Matteo Mattsteel Vitt...
matteo_vitturi
Aug 3, 2010 9:25 pm
Peter, ... I don't thing i understand very well what you're saying about 6n+/-1 that should represent all primes. When n=20 then 6n-1=119 and 6n+1=121 and both...
21688
Peter Kosinar
pkosinar
Aug 3, 2010 10:08 pm
Matteo, ... An expression (e.g. 2n+1) represents a set S if every number from set S can be written in the form prescribed by the expression. It's not necessary...
21689
Alberto Zelaya
albrtzlya
Aug 3, 2010 11:47 pm
If we can probe that there is a set that always will be denser than 6ab+-a+-b then twin primes will be infinite. I asked myself if it is possible to get a...
21690
Martin Aaronson
martin_aaronson
Aug 4, 2010 12:16 am
Peter Thanks for your comment. I admit I am wrong technically in that since 2 is the only even prime, I usually skirt around that issue by always prefacing...
21691
pbtoau
Aug 4, 2010 8:04 am
Congratulations on this accomplishment! I am looking forward to the paper describing the work. Is there a pre-print available? I do have two questions about...
21692
Chris Caldwell
primemogul
Aug 4, 2010 7:39 pm
Jens Franke (Universitat Bonn, http://www.math.uni-bonn.de/members?mode=struc) is not on this list. I just thought the item might interest some who are so...
21693
Martin Aaronson
martin_aaronson
Aug 5, 2010 10:35 am
Peter Thanks for your comment. I admit I am technically wrong in that since 2 is the only even prime, I usually skirt around that special case by always...
21694
bhelmes_1
Aug 5, 2010 4:18 pm
A beautifull evening I have tried to make a sufficent proof for all odd primes: http://beablue.selfip.net/devalco/suf_prime.html There remains two question: 1....
21695
w_sindelar@...
Aug 5, 2010 7:05 pm
Found no reference on the web. Will this statement hold up in the realm of huge numbers? In every occurrence of positive twin prime pairs P and Q=P+2, except...
21696
Jack Brennen
jbrennen
Aug 5, 2010 7:18 pm
Don't you mean that A and B are the larger members of those twin prime pairs? For any X of the form X = 6*k+/-1, note that (5*X^2-1)/4 will be of the form...
21697
Jack Brennen
jbrennen
Aug 5, 2010 7:27 pm
Also, with regard to the ending digit of 1, that's a consequence of: X == 6*k-1, (5*X^2-1)/4 == 15*k*(3*k-1) + 1 X == 6*k+1, (5*X^2-1)/4 == 15*k*(3*k+1) + 1 ...
21698
Tom Hadley
kctom99
Aug 5, 2010 8:15 pm
Bill, Jack wrote: "For any X of the form X = 6*k+/-1, note that (5*X^2-1)/4 will be of the form 6*m+1, so it can never be the smaller member of a twin prime...
21699
paulunderwooduk
Aug 5, 2010 10:11 pm
... Hi with the code: if numlib::jacobi (base, p)=-1 then break; end_if; base:=base+1; I think you are on to a winner using a *minimal* value. If you tested...
21700
w_sindelar@...
Aug 6, 2010 11:09 am
Jack Brennen wrote; "Don't you mean that A and B are the larger members of those twin prime pairs?" Yes, Jack that is what I meant. I mixed them up when I...
21701
bhelmes_1
Aug 8, 2010 6:00 pm
Dear Paul, ... Kermit Rose tested the algorithm for p up to 205401 with all possible "a". He did not find counterexample except a=p-1 for some p "Is it...
21702
djbroadhurst
Aug 8, 2010 7:46 pm
... The concept of "a cyclic group in the adjoined numbers", modulo a composite integer, has not been defined. In any case, the "proof" is clearly nonsense. It...
21703
djbroadhurst
Aug 9, 2010 12:00 pm
... What is your "strong witness" A for the probable primality of p = 170141183460469231731687303715884105727 ? David...
21704
bhelmes_1
Aug 9, 2010 2:12 pm
A beautifull day, ... The description of a cyclic group is borrowed from the cyclic group of natural numbers. I mean a cyclic group in the adjoined numbers...
21705
bhelmes_1
Aug 9, 2010 2:29 pm
Dear David ... p is prime with witness A=3, 3 is the smallest witness. Greetings from the primes Bernhard...
21706
djbroadhurst
Aug 9, 2010 2:53 pm
... If p is an odd prime, then the group (Z/Zp)* of integers from 1 to p-1 is cyclic under multiplication modulo p. If n is a square-free odd composite...
21707
djbroadhurst
Aug 9, 2010 3:06 pm
... Might you like to try again :-? David...
21708
bhelmes_1
Aug 9, 2010 6:38 pm
Dear David, ... p = 3 mod 4, therefore r=2, let a=3 (1+sqrt (3))^2 = (1+sqrt (3))*(1+(sqrt (3)) = 1*1+sqrt (3)*sqrt (3)+2*sqrt (3) = 4+2*sqrt (3) The result is...
21709
bhelmes_1
Aug 9, 2010 7:01 pm
Dear David, ... That´s right, but does not consider the ring with an adjoined square root. If p is an odd prime, then the group of natural numbers with an...
21710
djbroadhurst
Aug 9, 2010 8:29 pm
... I invited you to consider that simpler case in order to impress on you the importance of p being a prime. ... In this case you also begin with the crucial...
21711
bhelmes_1
Aug 9, 2010 8:29 pm
... First, there was a small error in the program, i wrote for 4. p-1 instead of p+1, i corrected it. You are right, that my program does not detect any...
21712
djbroadhurst
Aug 9, 2010 8:42 pm
... Wrong! In fact r = 2^127 and (1 + sqrt(3))^r = -2 mod p so a = 3 is not allowed, by your "criterion 4". Any advance on a = 3 ? David...
21713
Sebastian Martin Ruiz
s_m_ruiz
Aug 11, 2010 2:48 pm
Hello all: This is mi new web page (in spanish and english). http://www.numerosprimos.net/ sincerely Sebastián Martín Ruiz [Non-text portions of this message...
