Hi all, and Phil, and Milton: I have not seen much news about the "new" algorithm for Primes in P, recently. Which way is the wind blowing? Now, lets try not...
8517
Phil Carmody
thefatphil
Sep 1, 2002 8:28 am
... Because nothing much has changed in the last week or so. ... Agrawal, Kayal, and Saxena, Bernstein, Lenstra, Morain. Are you counting modulo 5 or...
8518
djbroadhurst
Sep 1, 2002 8:59 am
The most helpful piece of reporting that I have seen on the AKS algorithm and its context is at http://research.microsoft.com/~pleyland/primes/AKS.htm Thanks...
8519
djbroadhurst
Sep 1, 2002 12:11 pm
zeta(-k)/zeta(-1) is prime for k=25,33,37,73,117,673, what, if anything, comes next?...
8520
Yves Gallot
galloty@...
Sep 1, 2002 5:45 pm
... I don't think that François Morain improved the algorithm. His paper just indicates the proof of AKS theorem, the results of his implementation and a...
8521
Leonid Durman
leoniddurman
Sep 1, 2002 8:55 pm
Hello all, I have made small researches for page. Strong PRPs http://www.utm.edu//research/primes/prove/prove2_3.html I checked only two bases what to detect...
8522
djbroadhurst
Sep 1, 2002 9:30 pm
... Excellent! Maybe you could send this to Richard Pinch, via email address at http://www.chalcedon.demon.co.uk/rgep.html and tempt him into to spare-time...
8523
Phil Carmody
thefatphil
Sep 1, 2002 10:46 pm
... Great work, Leonid. I briefly looked at this problem in the past, but I restricted myself to a smaller set of bases, and discovered that I was almost...
8524
Jason Moxham
jasonmoxham
Sep 2, 2002 12:44 am
... some more examples for composite bases remember to check gcd(n,base)=1 bases 2 & 1226150 and n<38,210323 then n is prime 2 & 305185 and n<72,498253 and...
8525
purushaz
Sep 2, 2002 4:43 am
Thanks, Phil, for the previous proof on conjecture that if O(n) for p is odd, then O(n^2) is the same; otherwise, O(n^2) is half that of O (n). Eg. O(2) for 7...
8526
Leonid Durman
leoniddurman
Sep 2, 2002 6:48 am
Hello all, ... It still best practical results. I have spent only hour for search. But at the large expenditures of time and resources it is possible to...
8527
Phil Carmody
thefatphil
Sep 2, 2002 8:35 am
... You basically mean remember the last-but-one value in the SPRP test. ... If you could get those references I'd be grateful. I don't know exactly what you...
8528
djbroadhurst
Sep 2, 2002 9:34 am
I see that Jason used 2 & x & y ... That makes the problem rather easy up to n=10^13, since one can pinch the file ...
8529
ttpi314159
Sep 2, 2002 9:44 am
... I am puzzled,... probabilities?...
8530
Phil Carmody
thefatphil
Sep 2, 2002 10:07 am
... Wipe that smilie off your post, David. Jason has all 2 SPSPs up to 4,503,586,330,870,201 Pinch is _such_ a 20th century resource... Phil ===== "The hottest...
8531
djbroadhurst
Sep 2, 2002 10:38 am
... But the smilie was written _after_ studying http://217.35.81.229/spp.html so what joke is on whom, Phil? David (whose humour[?] is known to be perverse)...
8532
djbroadhurst
Sep 2, 2002 10:50 am
... Here zeta is Riemann's zeta function, which vanishes at the even negative integers and is rational at the odd negative integers, with zeta(-1)=-1/12. Primo...
8533
Max B
zen_ghost_floating@...
Sep 2, 2002 12:02 pm
Look at this-- A073694 Sequence: 5,32,50,162,512,1984,2450 Name: n such that the number of divisors of n = number of anti-divisors of n. ... What would "n...
8534
Sebastian Martin
sebi_sebi
Sep 2, 2002 12:22 pm
Hello all: you can see my article about prime numbers at: http://www.gallup.unm.edu/~Smarandache/SMRuiz-nextprime.pdf and other formulas at: ...
8535
djbroadhurst
Sep 2, 2002 12:30 pm
... Why stop at such small values? It takes little time to go up to n=10^5. By brute force: {A(n)=local(o);o=n;while(o%2==0,o=o/2); ...
8536
Phil Carmody
thefatphil
Sep 2, 2002 12:42 pm
... I've never liked slapstick. Phil ===== "The hottest places in Hell are reserved for those who, in times of moral crisis, preserved their neutrality." --...
8537
djbroadhurst
Sep 2, 2002 12:44 pm
Sebastian Martin re-advertised ... Here's what was said on another list when Sm*r*nd*ch* adverts became too frequent: ...
8538
djbroadhurst
Sep 2, 2002 1:22 pm
"Max B" asked ... The "excluding" is unnecessary, since 1 is not an anti-divisor. For what it's worth, I reckon that the sequence, up to 10^5, is 11 22 33 65 ...
8539
djbroadhurst
Sep 2, 2002 3:23 pm
Off-list, Max B asked for my code for this exercise. For what it's worth, this was it: {SA(n)=local(o);o=n;while(o%2==0,o=o/2); ...
8540
Jon Perry
jon_perryuk
Sep 2, 2002 5:28 pm
Purely for amusement - don't burn too many brain cells thinking about it: When is zeta(a+ib)/zeta(c+id) prime? Jon Perry perry@... ...
8541
Jon Perry
jon_perryuk
Sep 2, 2002 5:36 pm
Consider a k-tuple of consecutive positive integers, and define M as max{no.of factors of a_i} The basic conjecture is that if k-tuples with M<const exist,...
8542
paulunderwooduk
Sep 2, 2002 7:43 pm
Dear members, I have uploaded a very quick gmp program to see if f|x^f-x => f is Baillie-PSW probable prime (where f=x^3-x-1). Please check it is a valid...
8543
Phil Carmody
thefatphil
Sep 2, 2002 8:01 pm
... I nearly jumped on <<< while ( mpz_kronecker( d, f ) > 0 ); ... until I noticed it had a 'do' before it. (I'm a "} while" man). The following looks dodgy: ...
8544
Jason Moxham
jasonmoxham
Sep 2, 2002 8:41 pm
... This is what my current code is based on http://www.chalcedon.demon.co.uk/publish.html#41 Not read this yet , but it looks good ...
8545
djbroadhurst
Sep 2, 2002 11:37 pm
... As far as I can tell, the Baillie-PSW test was restricted to n = 2 or 3 (mod 5). What do you do in the other 50% of the cases? David...
