Fermat's Factoring Algorithm with the first digits of the factors known, can be done as on page 198 of Yan's book (Number Theory for Computing) with a...
5021
Paul Jobling
paul_joblinguk
Feb 1, 2002 9:15 am
... Indeed - the first GIMPS prime now appears to be within reach... Congratulations! Paul. __________________________________________________ Virus checked by...
5022
Phil Carmody
thefatphil
Feb 1, 2002 11:14 am
... Anyone care to do a scan/upload so that we can see the full details? (Or transcribe) ... A 'where' clause is usually intended to refine or clarify the...
5023
djbroadhurst
Feb 1, 2002 11:20 am
Phil: I think that Milton was here talking about how to use leading digits, not about how to find them. In this case he was suggesting how to make the very...
5024
paulmillscv
Feb 1, 2002 11:30 am
Hello, Good point Jud. The numeral 2 (a historical sociologically defined term) is distinct from the number 2. This is to say that the concept of 2 exists...
5025
Phil Carmody
thefatphil
Feb 1, 2002 12:28 pm
... Milton's previous posts hav claimed that he can predict the leading digits. This has been called into question many times by the several people whose names...
5026
djbroadhurst
Feb 1, 2002 12:48 pm
... So is there a range where Lehman's method (CP 5.1.2) is best? This is trial div up to n^(1/3) and then Fermat with multipliers up to n^(1/3). #ops =...
5027
Phil Carmody
thefatphil
Feb 1, 2002 1:28 pm
... It's a tough call. Lehman's method isn't really a single method, it's a combination of what is effectively an O(f(p)) method and a O(g(N)) method. In order...
5028
paulmillscv
Feb 1, 2002 2:37 pm
Hello, Re, the prime/physics post. The spectral analysis of integers is a way forward. However, number theorists are doing it already! The modulo operator is...
5029
Paul Leyland
pleyland@...
Feb 1, 2002 2:42 pm
... To be even more fair to Fermat, it's a pretty good algorithm if you know that the composite has precisely two factors and that they differ only slightly in...
5030
Yves Gallot
galloty@...
Feb 1, 2002 3:33 pm
... Not to human intellect. We know today that the chimpanzee is able to compute basic operations and has the knowledge of small numbers. I would not be ...
5031
djbroadhurst
Feb 1, 2002 5:01 pm
... It's a lousy bottom line, because it suggests that you have little experience of PrP hunting, Paul. One proceeds in 2 stages: sieve and then PrP test on...
5032
Jud McCranie
jud.mccranie@...
Feb 1, 2002 5:21 pm
... According to "The Mathematical Experience", by Davis and Hersh, page 334, "Russell and Whitehead ... after 362 pages, the arithmetic proposition 1+1=2 is...
5033
Jud McCranie
jud.mccranie@...
Feb 1, 2002 5:31 pm
... That's a very good point! +--------------------------------------------------------+ ... +--------------------------------------------------------+ ...
5034
David Litchfield
litchfield_d
Feb 1, 2002 6:03 pm
This is probably going to sound like a really dumb question with the answer being a resounding no, but, is there anyway, given a number which is the result of...
5035
djbroadhurst
Feb 1, 2002 6:12 pm
Yes the nipping in and out of 3-d idea was a bit corny. But I want to reinforce what Jud said about absolute indistinguishability in physics. In quantum...
5036
Jon Perry
jon_perryuk
Feb 1, 2002 6:35 pm
... ln x1y1z1 - ln x2y2z2 is minimum when x1y1z1-x2y2z2=2. Assuming this happens infinitely often, then ln x1y1z1 - ln x2y2z2 tends to zero. Jon Perry ...
5037
paulmillscv
Feb 1, 2002 6:36 pm
... Hello, It is nice to welcome someone with an interest in logic. ... Yes, but symbols of reality. Therefore the 3-d cartesian co-ordinate system is a real...
5038
Jon Perry
jon_perryuk
Feb 1, 2002 6:38 pm
If n=pq, and x=p+q, we can say x>=2sqrt(n), and x<(n/2)+2. I don't think there is anything else we can infer. ... If 20=p+q, what are p and q? And from this,...
5039
Jon Perry
jon_perryuk
Feb 1, 2002 6:41 pm
Automatic typo correction program spotted a typo in Jon Perry's email: RE:[PrimeNumbers]Dumb Question Please read: x<=(n/2)+2 for: x<(n/2)+2 Jon Perry ...
5040
David Litchfield
litchfield_d
Feb 1, 2002 6:52 pm
... Hmm. Shame. ... Well, the reason I say it's trivial is for this. Assume the number you've been given is say 51 and we want to work out p and q. If we knew...
5041
Jon Perry
jon_perryuk
Feb 1, 2002 7:24 pm
7,19,29,37,47,59,67,79,89,97,... 23,67,89,199,331,353,397,419,463,617,661,683,... 3,5,11,31,127,709,... 2,3,5,7,11,13,17,23,31,41,43,53,... What happens next? ...
5043
zwizard666
Feb 1, 2002 10:56 pm
Greetings: Thoughts of responses and goals of mathematics/perception: I was very pleased that paulmillscv realized exactly what I was "trying" to say. The...
5044
paulmillscv
Feb 1, 2002 11:02 pm
Hello, As requested by David, a verification of the new Milton Brown-Mills heuristic for a prime search of the form 12345*2^n +1 . (Not a GFN form, as...
5045
djbroadhurst
Feb 1, 2002 11:17 pm
... than what is this ten time faster, pray? David...
5047
J
fender_zar
Feb 2, 2002 4:24 am
Dear Colleagues, I never expected so many emails about the 3d coordinate system. I must thank everyone for contributing. In the original Email I sent to this ...
5048
Jon Perry
jon_perryuk
Feb 2, 2002 9:51 am
... Not what I had in mind. ... My Spanish is one of my weak points. Anyone care to translate? Jon Perry perry@... ...
5049
Jon Perry
jon_perryuk
Feb 2, 2002 10:42 am
Anyone seen this before? http://www.geocities.com/aj_thomas_w/WalkerEquation.html Jon Perry perry@... http://www.users.globalnet.co.uk/~perry ...
5050
djbroadhurst
Feb 2, 2002 11:21 am
Eq(22) at http://mathworld.wolfram.com/RiemannZetaFunction.html...
5051
djbroadhurst
Feb 2, 2002 12:06 pm
Primitive AP with same tau > 10^(10^100) Phil asked for some numbers and equations, to dilute the metaphysics. Here goes. Construction: Find a pair of titanic...
