Wojciech Izykowski has discovered AP19 with the smallest possible start of 19: 19 + 13234551541698967679 * 17# * n, n=0,...,18 (27 digits) At the moment it is...
24881
mikeoakes2
Feb 26, 2013 9:12 am
... An amazing and highly nontrivial discovery - many congratulations! But don't rush to look for an AP23: heuristics in my NMBRTHRY post of 2001 ...
24882
Jens Kruse Andersen
jkand71
Feb 27, 2013 5:36 pm
... Congratulations to Wojciech! http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart is updated with a mixed color entry to show that it has...
24883
bobgillson
Mar 3, 2013 4:04 pm
After a few restless nights, thinking about prime numbers, it finally dawned on me. . . Heuristically, every natural number, N, greater than 3, contains at...
24884
James Firth
cpu_core_mel...
Mar 4, 2013 10:20 pm
Hi, Forgive the intrusion as I'm a physicist with an interest in efficient computing rather than a mathematician who has studied number theory. In order to...
24885
Jack Brennen
jbrennen
Mar 4, 2013 10:39 pm
Take a look here: http://code.google.com/p/primesieve/ Looks like you can extrapolate that implementation to get the first 3.2 trillion primes in about 5-6...
24886
James Firth
cpu_core_mel...
Mar 4, 2013 11:35 pm
Thanks Jack, I'll take a look. RAM becomes an issue in my implementation at least because as x gets large then if the sieve 'slice' is too small one wastes...
24887
James Merickel
moralforce120
Mar 4, 2013 11:47 pm
I have been working on some compression notions regarding primes. If anybody has references on what's out there already on this matter, if what I am doing is...
24888
Phil Carmody
thefatphil
Mar 5, 2013 12:50 pm
... I think the results of a willy-waving contest nearly a decade ago between Terje Mathisen and James Van Buskirk on c.l.a.x, concluded that about an order of...
24889
Ben Buhrow
nebworhub
Mar 6, 2013 2:33 pm
... Nearly two orders of magnitude is possible. YAFU and primesieve both compute pi(x) to 3.2e12 using the sieve of Eratosthenes in about 30 minutes on my...
24890
Ben Buhrow
nebworhub
Mar 6, 2013 4:30 pm
... Apologies, I was confusing pi(1e14) ~= 3.2e12 with pi(3.2e12). After running some experiments, it looks like the two programs I mentioned will take about...
24891
James Firth
cpu_core_mel...
Mar 6, 2013 5:40 pm
Thank you Ben. I have already optimised down to 18 hours for pi(1e14) however primesieve is consistently running at least 4 times faster on my machine. I am...
24892
WarrenS
warren_d_smi...
Mar 6, 2013 9:42 pm
If you are programming a new sieve, I'd rather like it if you tried this so you could do something new. Naive Eratosthenes: runtime=NloglogN word-ops memory=N...
24893
viva8698
Mar 7, 2013 2:55 pm
Hi, I have a question where I need a very very reliable answer: Does there exist any function in the world to which I can input the first 6 prime numbers and...
24894
Maximilian Hasler
maximilian_h...
Mar 7, 2013 4:24 pm
... Did you google ? There are explicit formulae for prime(n) but they are inefficient to compute. For example, on...
24895
Phil Carmody
thefatphil
Mar 7, 2013 6:28 pm
... Please forgive my curtness, but have you read all the material by, for example, Sorenson? -- () ASCII ribbon campaign () Hopeless ribbon campaign ...
24896
WarrenS
warren_d_smi...
Mar 7, 2013 6:30 pm
My description included the wrong claim that step 3 would take asymptotically negligible time compared to (the big kahuna) step 2. My justification for that...
24897
WarrenS
warren_d_smi...
Mar 7, 2013 7:09 pm
... --no. However, prodded by you, I just looked at "The pseudosquares prime sieve" by Jonathan P. Sorensen 2006 and some other stuff he cites. The particular...
24898
djbroadhurst
Mar 8, 2013 2:47 pm
It is notable that http://physics.open.ac.uk/~dbroadhu/cert/gigantic.txt now contains 5 proofs of primality above 50k digits for which great effort was...
24899
WarrenS
warren_d_smi...
Mar 10, 2013 8:55 pm
//Code by Warren D. Smith, March 2013. Compiles with gcc. //Speed, on 2GHz intel gcc 4.2.1, is about 25 minutes to test 2^30 consecutive integers... //i.e....
24900
djbroadhurst
Mar 11, 2013 2:09 am
... Here are counts up to 2^n, for n = 32 to 52: [32, 50] [33, 77] [34, 125] [35, 187] [36, 251] [37, 330] [38, 455] [39, 618] [40, 851] [41, 1157] [42, 1557] ...
24901
djbroadhurst
Mar 11, 2013 4:18 am
... Here is a comparison of #spsp{2,63778} with #spsp{2,858945}, in the third column. These base-pairs start level at 2^32 and then play tag: [32, 50, 50] [33,...
24902
WarrenS
warren_d_smi...
Mar 11, 2013 4:36 am
If it is your goal to choose X so there are few spsp{2, X}, then X=735 does pretty well. There are 57 spsp{2, 735} below 2^32 and 1149508 spsp{2, 735} below...
24903
Phil Carmody
thefatphil
Mar 11, 2013 7:04 pm
... How many yield square roots of -1 that aren't the same (or additive inverses) from the two SPRP tests? ... Once you've got a SPRP, on average each new...
24904
WarrenS
warren_d_smi...
Mar 11, 2013 8:05 pm
... --don't understand question. ... --not so. I think you are right eventually (i.e. after you've done 9999 spsp tests to different random bases, the 10000th...
24905
WarrenS
warren_d_smi...
Mar 11, 2013 8:14 pm
... --Indeed, Thomas R. Nicely implemented the BPSW $620-640 test and reported "However, a BPSW test typically requires roughly three to seven times as many...
24906
djbroadhurst
Mar 11, 2013 8:49 pm
... column 1: n column 2: #spsp{2,735} up to 2^n column 3: #spsp{2,63778} up to 2^n column 4: #spsp{2,842774} up to 2^n column 5: #spsp{2,858945} up to 2^n ...
24907
Phil Carmody
thefatphil
Mar 11, 2013 9:33 pm
... Perhaps I was misremembering """ It has been proven ([Monier80] and [Rabin80]) that the strong probable primality test is wrong no more than 1/4th of the...
24908
djbroadhurst
Mar 11, 2013 9:52 pm
... I think that's a bound, not an estimate. ... In GP, I use Joerg Arndt's code from http://www.jjj.de/pari/rabinmiller.gpi and so, like Warren, do not use...
24909
David Cleaver
wraythex
Mar 11, 2013 10:10 pm
You can see a good post about using a single spsp test to prove any number < 2^32 prime/composite over on the mersenneforum: ...
