... Blowing my own trumpet: While no one knows a counterexample to the 1+2 selfridge BPSW, I have yet to find a counterexample > 10^13 to: (L+2)^(n+1)==2*x+5...
24915
djbroadhurst
Mar 12, 2013 12:46 am
... I have a hunch that BPSW may have been tested up to 2^64, if Jan Feitsma, and followers, have done their stuff aright? Note that 2^64/10^13 > 1844674 so...
24916
WarrenS
warren_d_smi...
Mar 12, 2013 1:48 am
... --you've got to stop describing this stuff in mysterious language nobody but you can understand. Well, maybe somebody follows, but I at any rate, have no...
24917
WarrenS
warren_d_smi...
Mar 12, 2013 1:55 am
... --My claims about infallibility up to 2^64 rely on a database compiled by Jan Feitsma of all strong psp(2) up to 2^64. Actually all fermat(2) pseudoprimes...
24918
paulunderwooduk
Mar 12, 2013 2:02 am
... Warren, for a definition of "a selfridge unit" please see: ...
24919
WarrenS
warren_d_smi...
Mar 12, 2013 2:35 am
... --this gives me a blank page. ... --this pdf file is called "unrepairably damaged" hence unreadable by my computer....
24920
David Cleaver
wraythex
Mar 12, 2013 2:44 am
... Actually, Jeff Gilchrist and I performed the double check on the data. I wrote the majority of the double-checking code, which was independent of Jan's...
24921
Phil Carmody
thefatphil
Mar 12, 2013 9:34 am
... Help a thicko out - what's the line 90119 180239 supposed to mean in Jan's post? Flinging those numbers at GP... ? Mod(2,90119)^(90119-1) Mod(35397, 90119)...
24922
Phil Carmody
thefatphil
Mar 12, 2013 10:27 am
... A "selfridge" is the cost of a single (S)PRP test - i.e. a modular exponentiation modulo p with Omega(lg(p)) mulmod steps. Optimising the squarings into...
24923
David Cleaver
wraythex
Mar 12, 2013 10:10 pm
... Those two numbers are one (r,p) pair. ... Here's an excerpt from an email from Jan: "The (r,p)-pairs are used to find all pseudoprimes n=p*s with a large...
24924
Phil Carmody
thefatphil
Mar 13, 2013 10:47 am
... They're basically just a shallow (by p) but wide (by r) extension to the Cunningham tables for 2? How big are the (r,p) tables for the E case? (And how...
24925
Phil Carmody
thefatphil
Mar 13, 2013 11:31 am
What property is shared by these numbers : 63, 117, 171, 275, 315, 333, 441, 513, 549, 585, 603, 657, 693, 711, 775, 819, 825, 855, 873, 927, 981, 999, ... ...
24926
djbroadhurst
Mar 13, 2013 12:21 pm
... These appear to be been studied with due care: http://www.janfeitsma.nl/math/psp2/wieferich David...
24927
Maximilian Hasler
maximilian_h...
Mar 13, 2013 12:49 pm
... see also https://oeis.org/A158358 ... Thanks for the link, I'll add it to the above OEIS record. Maximilian [Non-text portions of this message have been...
24928
Maximilian Hasler
maximilian_h...
Mar 13, 2013 12:59 pm
... do you type rot13 by hand ?! M. [Non-text portions of this message have been removed]...
24929
djbroadhurst
Mar 13, 2013 1:10 pm
... A slight improvement is obtainable by using a smoother base: 1147253 spsp{2, 3*5^5} below 2^64. David...
24930
Phil Carmody
thefatphil
Mar 13, 2013 3:14 pm
... I'm happy with category E, but am less happy with category S presently. Where the wieferich cases refer to category S, I'm only as happy with those as I am...
24931
Walter Nissen
nissen@...
Mar 13, 2013 6:44 pm
Lotta baggage in that URL ! And page 1 _is_ often blank . Paul , check out to which page you desire to refer . Then replace the final "1" in this URL : ...
24932
mrsinclair
Mar 13, 2013 9:05 pm
Hi, first post, I have developed a formula for checking divisibility of numbers but need verification before I start using computers to test speed of the...
24933
djbroadhurst
Mar 13, 2013 11:11 pm
... By making it freely available to all and then hoping that someone might take the care to examine it. David...
24934
Chris Caldwell
primemogul
Mar 14, 2013 12:47 am
... Absolutely! In math you stake you ownership of a result by sharing it. Note that you increase the chances of getting your result examined if you write...
24935
WarrenS
warren_d_smi...
Mar 14, 2013 1:46 am
... --ok, so if I (Warren D. Smith) understand aright, Jan Feitsma did eventually describe his algorithm in a way other than just providing his program (i.e....
24936
djbroadhurst
Mar 14, 2013 2:41 am
... Ah, thanks for clarification. Please keep on examining category S. I'm otherwise engaged, but shall try to keep up reading. With thanks to David Cleaver,...
24937
djbroadhurst
Mar 14, 2013 2:55 am
... Thanks, Warren, for your effort and opinion. I forgive your tone. David...
24938
Phil Carmody
thefatphil
Mar 14, 2013 11:10 am
... That indeed was one of my sources of unhappiness. ... Even after having an aha! moment reading your wonderfully clear explanation, I went back to the...
24939
WarrenS
warren_d_smi...
Mar 14, 2013 4:02 pm
Some slight updates. 1. One advantage of my "new" suggested procedure based on backtrack would be, it would enumerate every pseudoprime exactly once, so in...
24940
paulunderwooduk
Mar 14, 2013 4:29 pm
http://www.newscientist.com/article/dn23171-largest-fake-prime-number-holds-300-billion-digits.html Does anybody volunteer to run BPSW on this number?...
... Let a=2^(2^57885161-1)-1 and b=(a+2)/3. Then N=a*b is 2-PRP. Is N a BPSW PRP? Who could possibly tell? Who might ever care? David...
24943
paulunderwooduk
Mar 15, 2013 12:38 am
Hi, perhaps the gremlins will like this puzzling composite test. For non-square n coprime to 30 find x and a: kronecker(x^2-4,n)==-1 gcd(x^3-x,n)==1 ...
