... In general, finding a square root modulo a composite, m, is as difficult as factorizing m. If someone could do one of these things in polynomial time, they...
7746
Phil Carmody
thefatphil
Oct 1, 2006 10:04 am
That would conventionally be "modular", not "modulus". Posted by: "Kermit Rose" kermit@... kermit1941 ... No matter what algorithm you use (it's...
7747
Robert
robert44444uk
Oct 1, 2006 6:58 pm
... There has been a delay since this was posted. Regarding the Sierpinski case: One such covering set is [13,5,7,41,73,17,193,6481,97,577] which have ...
7748
David Broadhurst
djbroadhurst
Oct 1, 2006 10:45 pm
... I translated it to GP. Here is a typical random run with a small composite modulus: No sqrt of Mod(2437846,10097063) because of loop. No sqrt of...
7749
David Broadhurst
djbroadhurst
Oct 1, 2006 10:53 pm
... Please send it to Neil, with "mooted" ==> conjectured. Nice work with a=3, thanks, Robert. David...
7750
Robert
robert44444uk
Oct 2, 2006 9:36 am
... Done and dusted, although I am no expert on finding suitable references Regards Robert Smith...
7751
David Broadhurst
djbroadhurst
Oct 2, 2006 10:03 am
... Did you remember to multiply 36785490291994693 by 2 ? David...
7752
Robert
robert44444uk
Oct 2, 2006 10:18 am
... Defined it in a different way, so that each of the numbers in the series must be multiplied by all primes with multiplicative order base b of 1 to get to a...
Hi, All LLR/LLRNET users, I wish to remind you of the real features of these programs : While testing k*b^n+1 or k*b^n-1 candidates, LLRNET/LLR can only prove ...
7754
Kermit Rose
kermit1941
Oct 3, 2006 2:21 am
... Thanks David. I averaged the step length of the 8 successful runs you did, to get an average of 1700, which is slightly more than half the square root of...
7755
David Broadhurst
djbroadhurst
Oct 3, 2006 10:04 am
... For the case r=2 and k=1, see Cohen, CCANT, Algorithm 1.5.1. As Phil remarked, there are better methods when p != 1 mod 8, or p = 1 mod 2^e with large e. ...
Hello all, can everbody make a PRP-test with PFGW.exe (PFGW Version 20020515) for number "3*20000#-1" ? I don't care number is prime or not. I need the time in...
7758
jandersonlee
Oct 4, 2006 6:25 pm
ABC2 (1405659596+$a*55680004)*349#+1 a: from 0 to 10 step 1 newpgen and pfgw plus custom ap.c sieve Jeff Anderson-Lee...
7759
Norman Luhn
nluhn
Oct 4, 2006 9:56 pm
Big congratulations from me to your new AP record ! Norman ... ___________________________________________________________ Telefonate ohne weitere Kosten vom...
7760
David Broadhurst
djbroadhurst
Oct 6, 2006 2:22 pm
... Indeed. But that fact is not appreciated here: http://mersennewiki.org/index.php/Sierpinski/Riesel_Base_5 ... Maybe George should append a health warning...
7761
Jean Penné
jpyah2001
Oct 6, 2006 2:55 pm
... Thanks, David! I think this page might to be updated... I posted a warning in a thread of this project's forum : ...
7762
avrelian
Oct 7, 2006 2:29 am
Could somebody tell me about validity of this assertion: if gcd(x,y)=1 then such A and B exists that Ax-By=1 Thank you in advance...
7763
ramsey2879
Oct 7, 2006 3:56 am
... The proof is based upon the Chinese remainder therom and there are a number of web sites which discuss it....
7764
brockenlau
Oct 11, 2006 5:52 pm
Hello, I would like to know if anyone know how to set the range of one variable based on another variable. I tried to find generalized cullen and woodall...
7765
Steven Harvey
harvey563
Oct 11, 2006 7:03 pm
I suggest that you read the ABC format document. Example, for generalized woodall, ABC2 ($a+$b)*$a^($a+$b)-1 a: from 3 to 100 b: from 1 to 100 If you are...
7766
David Broadhurst
djbroadhurst
Oct 12, 2006 2:35 am
I just heard a remarkable radio programme on the BBC world service: http://www.bbc.co.uk/worldservice/programmes/discovery.shtml ... wherein Greg Chaitin...
7767
cino hilliard
hillcino368
Oct 13, 2006 7:00 pm
Hi, I have been looking at PRP's of the form 109999...91,109999...93,109999...97 using ABC2 10*(10*10^$a+10^$a-1)+m a: from 1 to 5000 where m=1,3,7 Some...
7768
Paul Underwood
paulunderwooduk
Oct 14, 2006 4:51 am
... Thanks for that, David. Omega is very interesting. http://www.youtube.com/results?search_query=Gregory+Chaitin&search=Search might be entertaining for...
7769
David Broadhurst
djbroadhurst
Oct 17, 2006 4:25 pm
... The form 11*10^n-k with k=3,7,9 requires ECPP for n=O(5000). You might obtain a Primo proof for 11*10^4983-9 is Fermat and Lucas PRP! in (very) roughly 3...
7770
cino hilliard
hillcino368
Oct 17, 2006 11:27 pm
... c:\pfgw>pfgw -tc -q11*10^^4983-9 PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 11*10^4983-9 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running...
7771
David Broadhurst
djbroadhurst
Oct 18, 2006 12:35 am
... At nearly 5000 digits, GP's APRCL may not finish in your lifetime. And I am wishing you a long life :-) David...
7772
cino hilliard
hillcino368
Oct 18, 2006 3:55 am
... Thanks. I wil let my cpus persue other tasks. Cino...
7773
jbohanon3
Oct 18, 2006 12:25 pm
I know this question has been asked before, but has any progress been made on getting a buildable source for the Linux version of PFGW? I recently got 1000...
7774
leavemsg1
Oct 18, 2006 1:08 pm
Hello, Group. It took about 3-4 minutes to find and less than 8 seconds to prove it. Is it prime? Z= ...
