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Old 2003-11-18, 01:07   #1
pakaran
 
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Aug 2002

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Default From the closed "new factor" thread...

Quote:
Here's a different problem. The primitive part of M(36960) is a 2312 digit probable prime. Dario Alejandro Alpern's java ECM, modified to allow larger numbers, confirmed that it is a probable prime for every base below 829 before I shut it down. Is Primo the best way for non-Americans to prove this is prime? How long would it take?

Here's the number for anyone interested:

813529538023299891949566022136256103776665445684570138851596
100348916821985995574880167952339915737438757662865532842333
679533155985198770019618570986494031038501487866267328946720
864188425165436148600051512954443291738035627474333187707736
064507785819357328549744383254423817437755425393531988204243
913282429414175711230497834650388103429517629650447863884587
070099692500108587002644925053521773552642119720405227714049
797193819869965261620934470986275684828939270790481739133859
336714719637484930604187819264316000660099099707381198022842
913331714433878275680235385806558857339412407703370475899517
988271999486359536909379670092590966098124708296402822298637
004728549319410359668092215189313384121826424609975178127402
128097073482973281703401007138281254322556739106825002662520
302580329441308435426088056958622683666789127694710679924407
148566345002318133042719318702083674231430888060802209742534
629195831164545756944721870800064227274553190671605086228942
882766761800822847853147785217394394521352945824664677293817
330393968175408931362378078090978598168816718627266587833118
654299814052970580043089045487153163726567778292413738181776
671955733912387716268675417210592423093871730571667805256172
589519712942535181125732773387771072113263978141203143854564
966027890131779556365495546154906118808766562202445346693562
594884865180959135122810474805021198366713035936666999070668
355416880575225014422400782008005254913394411698399343173794
268745206860707504575831684949715740170323069604876698998705
386257414455426476635291678747396836274840680624708850840393
950495068365079090464858886421629582404803475970407344916144
794827862915534055130493356262615804510533276900855923031467
881435148865541215522111586039751156192857592085031922809324
528284432944594548210933186319178405806610782276894699744744
638378355612128263672764097433998525704917358738689617648345
340706053020649487777839242058207296932455451899651062135342
726527987792324356630527942670782232350358877235807194075407
020187194833714413876570921651944736792221621740427861606442
257093811371968066311055141349268425067364225844804029368081
360544511889599768804397866249190845060763383462045413592832
148719459726485404628725833429048418085539070341527503467026
767411018850564995460393158145961670282298514626466414795954
87967333008211929296531424870401
If this still needs to be done, I can run it with primo. It would take about fifteen hours, no big deal.
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Old 2003-11-18, 01:10   #2
pakaran
 
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Actually, if anyone wants work done on testing PRPs below say 3500 digits, I'd be willing. I'm mostly doing GIMPS now, or I'd help out with the factoring work.
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Old 2003-11-18, 05:09   #3
antiroach
 
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this number has already been proven prime several months ago.
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Old 2003-11-18, 05:33   #4
wblipp
 
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"William"
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Quote:
Originally posted by pakaran
Actually, if anyone wants work done on testing PRPs below say 3500 digits, I'd be willing. I'm mostly doing GIMPS now, or I'd help out with the factoring work.
For the example you quoted, a primality certificate has already been created - it's later in that thread.

Will Edgington's factoredM.txt has 209 factors that are only PRP. Four of these are 11-smooth exponents, although only two are factors of 3326400. The smaller of these, M(15400), is 1455 digits. It is

(2^(385*20)+1)/(2^(77*20)+1)*(2^(11*20)+1)/(2^(55*20)+1)*(2^(7*20)+1)*(2^(5*20)+1)/((2^(35*20)+1)*(2^(1*20)+1))

If you need a decimal expansion you can get it from Dario's Java Factoring applet
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Old 2003-11-18, 06:48   #5
pakaran
 
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Quote:
Originally posted by wblipp
For the example you quoted, a primality certificate has already been created - it's later in that thread.

Will Edgington's factoredM.txt has 209 factors that are only PRP. Four of these are 11-smooth exponents, although only two are factors of 3326400. The smaller of these, M(15400), is 1455 digits. It is

(2^(385*20)+1)/(2^(77*20)+1)*(2^(11*20)+1)/(2^(55*20)+1)*(2^(7*20)+1)*(2^(5*20)+1)/((2^(35*20)+1)*(2^(1*20)+1))

If you need a decimal expansion you can get it from Dario's Java Factoring applet
Ok I can run that now, it'll be about an hour. I think Primo can parse that by itself.

If I go to sleep, I'll post in the morning. Do you want the cert (which may be a good fraction of a meg) pasted in here, or emailed to someone?

Nathan
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Old 2003-11-18, 07:01   #6
pakaran
 
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Oh, in that FactoredM.txt file, how do you tell which factors are only PRP? It seems they aren't distinguished in the formatting.
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Old 2003-11-18, 11:26   #7
smh
 
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If i understood things correctely, a lowercase 'd' means a number is 'done' and the cofactor pseudo prime to at least one base other than 2.
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Old 2003-11-18, 13:45   #8
ET_
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I can certificate the number with Primo, if you tell me to.

Luigi
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Old 2003-11-18, 14:44   #9
wblipp
 
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Quote:
Originally posted by pakaran
Ok I can run that now, it'll be about an hour. I think Primo can parse that by itself.

If I go to sleep, I'll post in the morning. Do you want the cert
(which may be a good fraction of a meg) pasted in here, or emailed to someone?

Nathan
Email the certificate to me for ElevenSmooth credit. You can also send it directly to
Will Edgington or rely upon me do that.

The other PRP within the ElevenSmooth domain was a surprise to me last night. A while
back Sander did some extensive work on M(26400) using Prime95. That primitive is the
other PRP. One drawback of the Prime95 approach used in the Special Project is that
we don't automatically notice these PRPs.

This one is slightly larger at 1886 digits:
(2^(165*80)+1)/(2^(55*80)+1)*(2^(11*80)+1)/(2^(33*80)+1)*(2^(5*80)+1)*(2^(3*80)+1)/((2^(15*80)+1)*(2^(1*80)+1))/1214401/994971331201/241967783549391442012801
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Old 2003-11-18, 18:35   #10
pakaran
 
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Ok, it's finished and I'm working on the second one. What's your email?
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Old 2003-11-18, 18:42   #11
pakaran
 
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Oh, and I don't see how failure to automatically spot PRPs is a major issue - running every cofactor ever generated by elevensmooth through pfgw would take under 2 minutes, probably well under with a SSE2 system.
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