While programing a comment lint for the new database system an old question has come up. In the past we have let "ECPP" be an archivable class. With some...
10601
Phil Carmody
thefatphil
Jan 1, 2003 6:02 pm
... As we recently witnessed. ... Is it a property of the number or the proof? If a property of the number, then ECPP and APRCL classes contain the same ...
10602
paulunderwooduk <p...
paulunderwooduk
Jan 1, 2003 7:13 pm
please see OP: http://groups.yahoo.com/group/primenumbers/message/8856 I have tested 1<x<=10^11 (4,772,369,646 PrPs). Many thanks to Michael Angel who tested...
10603
qntmpkt <qntmpkt@....
qntmpkt
Jan 2, 2003 5:09 am
... Re: Table #48 in Beiler's book on "least exponents" i.e. ORDER of p, to any base, e.g. ORD4 (7) = 3 or 4^3 == is congruent to 1 MOD 7. Thus, 3 is the...
10604
Paul Leyland
pleyland@...
Jan 2, 2003 8:59 am
... You may wish to consider what the factoring community does in analgous cases. It's occasionally the case that a factorization is found by two methods...
10605
Jason Moxham
jasonmoxham
Jan 2, 2003 9:56 am
A new version availible here http://217.35.81.229/gmp/prime1.15.tar.bz2 which corrects some minor bugs , thanks to Phil Carmody NOTE: This should still be...
10606
Gary Chaffey
garychaffey
Jan 2, 2003 12:18 pm
... I'm curious if there's anything special about the ... I have also looked at these factors.. It seems and this is only a conjecture that Let a1<a2 then if...
10607
Phil Carmody
thefatphil
Jan 2, 2003 1:10 pm
... There are three kinds of bugs: 1) Bugs that can make a prime number be declared composite 2) Bugs that can make a composite number be declared prime 3)...
10608
Jason Moxham
jasonmoxham
Jan 2, 2003 2:51 pm
... The recently corrected bug was type 3 , although as it was rare it acted like type 1 ... No specific reason , except the usual bugs that are in any program...
10609
David Broadhurst <...
djbroadhurst
Jan 2, 2003 5:47 pm
... 1) ECPP is at present an archivable class, with a top-20. I believe that it should stay like this, with Chris trying to chase up the folk in Marcel's...
10610
David Broadhurst <...
djbroadhurst
Jan 2, 2003 6:08 pm
... Maybe Marcel could try to encourage his top-20 to contact Chris? Congrats to Jeff Heleen: http://www.ellipsa.net/pages/primotop20.html (10^4769 - 1) / 3 -...
10611
David Broadhurst <...
djbroadhurst
Jan 2, 2003 7:48 pm
http://listserv.nodak.edu/scripts/wa.exe?A2=ind0301&L=nmbrthry&P=R2 has an interesting variant on the Sierpinski problem from Sun Zhi-Wei (of Wall-Sun-Sun...
10612
David Broadhurst <...
djbroadhurst
Jan 2, 2003 8:26 pm
Comment: Since Payam's PrP 19249+2^551542 is effectively unprovable, Prof. Sun Zhi-Wei's appeal is essentially directed at SoB, telling them that if/when...
10613
David Litchfield
litchfield_d
Jan 3, 2003 1:20 am
Hello all and happy New Year, Could someone tell me, please, if this "stands up"? All odd numbers of the form (a^2 + b^2) / 2 with both a and b being odd, that...
10614
Phil Carmody
thefatphil
Jan 3, 2003 1:33 am
... (03:22) gp > (a^2+b^2)/2 - (((a+b)/2)^2+((a-b)/2)^2) %1 = 0 i.e. if n=(a^2+b^2)/2, then n=(((a+b)/2)^2+((a-b)/2)^2) Phil ===== The answer to life's mystery...
10615
Phil Carmody
thefatphil
Jan 3, 2003 1:53 am
... It means I'm running The PARI Group's "gp" package at 3:22am. It's free, it's incredibly powerful, and it answers these kinds of questions without even...
So we can write: (a+b)/2)^2+((a-b)/2)^2 =a^2/4 + ab/2 + b^2/4 + a^2/4 - ab/2 + b^2/4 =a^2/2 + b^2/2 Jon Perry perry@... ...
10618
Phil Carmody
thefatphil
Jan 3, 2003 12:37 pm
... http://www.bookfinder.com/ has access to a wider selection of books, but with the drawback that you have to pay for them (which is after all what makes...
10619
Jon Perry
jon_perryuk
Jan 3, 2003 12:37 pm
Briefly: forprime (p=1000000,1000500, ep=eulerphi((p-1)*(p+1));print1(ep":"ep/(p^2-1)*1.0",")) indicates 0.22~< phi(p^2-1)/(p^2-1) <~0.33 leading one to the...
10620
Paul Leyland
pleyland@...
Jan 3, 2003 1:07 pm
... I don't see why your belief is justified based on a small sample and no analysis. Just because a function is bounded over a small range doesn't mean it...
10621
Jon Perry
jon_perryuk
Jan 3, 2003 8:58 pm
It was actually a fish for some voluntary labour. Pari chokes on primes>1000000, and I have no other means of performing such high powers tests that would be...
10622
richard_heylen <ri...
richard_heylen
Jan 3, 2003 9:00 pm
Has anyone heard of any conjectures similar to the following ones I have come up with? Conjecture: For real x>1 the smallest n such that there's always a prime...
10623
Phil Carmody
thefatphil
Jan 3, 2003 9:14 pm
... Use 'calc' instead. Or bc. Or the other 'calc'. Or use gp and use 'p=nextprime(p+1)' rather than 'forprime(p='. ... One of (p-1) and (p+1) is divisible by...
10624
David Broadhurst <...
djbroadhurst
Jan 3, 2003 9:14 pm
Jon Perry mistakenly claimed that ... Invoke it with -p10000000 to precompute primes to 10M. Limit is about 430M, as I recall, but then you need to allocate...
10625
David Broadhurst <...
djbroadhurst
Jan 3, 2003 9:36 pm
... .......................? No. p=3 gives 1/2 and p=2 gives 2/3 which is maximal, for prime p....
10626
Carl Devore
carldevore
Jan 3, 2003 9:49 pm
I am doing some timing tests in Maple in order to hunt down some bugs in its large-integer computation. It would be useful if I had primes close to 2^(2^n)...
10627
David Litchfield
litchfield_d
Jan 3, 2003 10:09 pm
I'm sure this must fall down - can someone confirm pointing out where? Cheers, David All primes of the form 4n+1 are the sum of two squares For every odd...
10628
paulunderwooduk <p...
paulunderwooduk
Jan 3, 2003 10:28 pm
... bugs in ... close ... found ... primes. ... running PFGW -f ABC2file 2^(2^14)+2775 is 2-PRP! (1.480000 seconds) 2^(2^13)+897 is 2-PRP! (0.280000 seconds) ...
10629
Phil Carmody
thefatphil
Jan 3, 2003 10:28 pm
... I don't know any list which goes up to such high powers of 2. Heheh, 2^(2^9) I could give you a vast number of examples for. You could generate PRPs using...
