[QUOTE=CRGreathouse]It takes time to run and I need to change the way it records its data. I'm not sure that I can do that today -- I have a big project to work on. (It would only take 15 minutes... but I don't have 15 minutes.) Why don't you write it and we can compare numbers tomorrow.
[/QUOTE]

Oki. I'll get working on it. Cheers.

Sorry about cutting out early. Preliminary results looked good, but I don't trust data averaged that way. Still not sure what's best... median, geomean, percentage at or above some threshold...?

[QUOTE=CRGreathouse]Sorry about cutting out early. Preliminary results looked good, but I don't trust data averaged that way. Still not sure what's best... median, geomean, percentage at or above some threshold...?
[/QUOTE]

Mean, and repeat it over and over, to ensure that it is not random outcomes, or alternatively, to show that it was merely random outcomes.

I was able to get a list of the bases a number is pseudoprime to going...

Though a decent check reveals that the 2nd-kind Cunninghams by far outperform their general counterparts in how many bases they are pseudoprime to. The general composites usually had no false witnesses when checked, besides 1.

[QUOTE=3.14159;224764]Mean, and repeat it over and over, to ensure that it is not random outcomes, or alternatively, to show that it was merely random outcomes.[/QUOTE]

You'll need to repeat it a huge number of times to make that work -- at least a billion, by my estimates.

[QUOTE=CRGreathouse]You'll need to repeat it a huge number of times to make that work -- at least a billion, by my estimates.
[/QUOTE]

Are you sure of that?

[QUOTE=3.14159;224774]Are you sure of that?[/QUOTE]

No, just an estimate. But I'm pretty sure you can't get reliable data, statistically speaking, by taking the mean for this problem with less than a million numbers. My heuristic for the size and variablility suggested a few hundred million as the right size.

[QUOTE=science_man_88;224688][CODE]6np+/-p 24m+7
└────┬────┘
Equations(m's) A002450 or A121290
[INDENT] └────┬────┘[/INDENT][INDENT] Mersenne Primes
[/INDENT][/CODE]

best I can do is a picture translation.

according to what you say:

[CODE]p 6n+1
└────┬────┘
n that work to primes[/CODE][/QUOTE]

you said for the p and 6n+1 case we were sieving p against 6n+1 and it leaves n for primes.

so that's what the:

[CODE]p 6n+1
└────┬────┘
n that work to primes[/CODE]

is

now if we use this logic what:

[CODE]6np+/-p 24m+7
└────┬────┘
Equations(m's) A002450 or A121290
[INDENT] └────┬────┘[/INDENT][INDENT] Mersenne Primes
[/INDENT][/CODE]

means is 6np+/-p sieve 24m+7 leaves Equations(m's)

Equations(m's) sieve A002450 or A121290 leaves Mersenne primes(indexes that give) . have i made sense yet ?

Anyone have any idea how to save your programs, so I don't have to continuously keep defining them every time I open PARI/GP?

[QUOTE=3.14159;224784]Anyone have any idea how to save your programs, so I don't have to continuously keep defining them every time I open PARI/GP?[/QUOTE]

maybe like CRG suggest we should all make scripts to write it to file and then read from the file the next time we open it I haven't done it yet but it should help lol.

To axn: Here's another wonderful pseudoprime number for you: 9479779630110266401 is pseudoprime to bases: 10, 17, 24, 36, 40, 54, 59, 60, 61, 68, 77, 90, 96, 98, 100, 102, 109, 127, 135, 139, 147, 150, 151, 153, 160, 179, 199, 203, 216, 218, 236, 242, 244, 247, 250, 254, 255, 263, 272, 278, 281, 287, 289, 299, 308, 319, 327, 341, 347, 349, 358, 360, 371, 375, 381, 384, 392, 397, 398, 406, 417, 425, 431, 433, 434, 436, 443, 451, 462, 479, 486, 497, 508, 523, 526, 531, 537, 545, 549, 553, 554, 556, 562, 563, 571, 574, 576, and 583.

Meh, there's no point in that, as I can collect an infinite amount of these.

Here are just a few pseudoprime numbers to catch:

[code]42619430701 * 85238861401 = 3632831746512063272101
42688800001 * 85377600001 = 3644667291008066400001
42902244001 * 85804488001 = 3681205080599778732001
43056990901 * 86113981801 = 3707808930854536592701
43094343601 * 86188687201 = 3714244900759004950801
43217073901 * 86434147801 = 3735430953085773641701
43547912101 * 87095824201 = 3792841296669296556301
43627953601 * 87255907201 = 3806796670778389780801
43857405901 * 87714811801 = 3846944104686281837701
43894758601 * 87789517201 = 3853499665236232195801
44033497201 * 88066994401 = 3877897751456916171601
44102866501 * 88205733001 = 3890125667165953099501
44332318801 * 88664637601 = 3930708980502663836401
44396352001 * 88792704001 = 3942072141948997056001
44524418401 * 89048836801 = 3964847667850090375201
44945970301 * 89891940601 = 4040280492551802090901
45164750401 * 90329500801 = 4079709357524094571201
45223447501 * 90446895001 = 4090320407706182842501
45410211001 * 90820422001 = 4124174526265272633001
45452899801 * 90905799601 = 4131932200594038779401
45490252501 * 90980505001 = 4138726145163983257501
45570294001 * 91140588001 = 4153303390629582882001
45687688201 * 91375376401 = 4174729706257901544601
45783738001 * 91567476001 = 4192301330642639214001
46039870801 * 92079741601 = 4239339406699504892401
46098567901 * 92197135801 = 4250155925000116523701
46215962101 * 92431924201 = 4271830305795920706301
46237306501 * 92474613001 = 4275777024888596419501
46424070001 * 92848140001 = 4310388550869072210001
46482767101 * 92965534201 = 4321295274685133121301
46573480801 * 93146961601 = 4338178227795657722401
46605497401 * 93210994801 = 4344144775942630012201
46722891601 * 93445783201 = 4366057199070869794801
46893646801 * 93787293601 = 4398028220546981420401
47048393701 * 94096787401 = 4427102699641544561101
47213812801 * 94427625601 = 4458288238368529118401
47240493301 * 94480986601 = 4463328414596411259901
47325870901 * 94651741801 = 4479476113028911232701
47379231901 * 94758463801 = 4489583231010092915701
47448601201 * 94897202401 = 4502739511815628683601
47507298301 * 95014596601 = 4513886783672887674901
47742086701 * 95484173401 = 4558613685083860040101
47811456001 * 95622912001 = 4571870649823306368001
47891497501 * 95782995001 = 4587191065728686992501
47939522401 * 95879044801 = 4596395616024022087201
48355738201 * 96711476401 = 4676554833878945694601
48665232001 * 97330464001 = 4736609611373643696001
48745273501 * 97490547001 = 4752203377325840320501
48964053601 * 97928107201 = 4794957090034238080801
49988584801 * 99977169601 = 4997717220763547834401
50143331701 * 100286663401 = 5028707428102879775101
50436817201 * 100873634401 = 5087745058683742131601
50516858701 * 101033717401 = 5103906025983081956101
50527530901 * 101055061801 = 5106062757852492212701
51311937601 * 102623875201 = 5265829880686523332801
51616095301 * 103232190601 = 5328442588192212465901
51642775801 * 103285551601 = 5333952584813059607401
51685464601 * 103370929201 = 5342774501990762713801
51781514401 * 103563028801 = 5362650467270159263201
51824203201 * 103648406401 = 5371496074785253089601
52224410701 * 104448821401 = 5454778146081222212101
52341804901 * 104683609801 = 5479329080536353434701
52576593301 * 105153186601 = 5528596326224939559901
52629954301 * 105259908601 = 5539824179398066842901
52656634801 * 105313269601 = 5545442377079111984401
52795373401 * 105590746801 = 5574702905049241240201
52886087101 * 105772174201 = 5593876417656231081301
52992809101 * 105985618201 = 5616475632777064047301
53136883801 * 106273767601 = 5647056840108815531401
53264950201 * 106529900401 = 5674309839776754930601
53377008301 * 106754016601 = 5698210030276668804901
53873265601 * 107746531201 = 5804657492977906516801
54390867301 * 108781734601 = 5916732891455591181901
54470908801 * 108941817601 = 5934159811159247606401
54807083101 * 109614166201 = 6007632716025032469301
54977838301 * 109955676601 = 6045125408446827294901
55004518801 * 110009037601 = 6050994177004120436401
55965016801 * 111930033601 = 6264166211016459530401
56274510601 * 112549021201 = 6333641086707848251801
56584004401 * 113168008801 = 6403499108048190733201
56674718101 * 113349436201 = 6424047343598959374301
56680054201 * 113360108401 = 6425257088399915442601
56770767901 * 113541535801 = 6445840176081653123701
57106942201 * 114213884401 = 6522405695039602506601
57288369601 * 114576739201 = 6563914583024273428801
57512485801 * 115024971601 = 6615372045962940737401
57581855101 * 115163710201 = 6631340073687537585301
57640552201 * 115281104401 = 6644866516014771336601
57688577101 * 115377154201 = 6655943855818354551301
57747274201 * 115494548401 = 6669495355233213102601
58424958901 * 116849917801 = 6826951645108653296701
58515672601 * 117031345201 = 6848167879836328537801
58675755601 * 117351511201 = 6885688590637889986801
58819830301 * 117639660601 = 6919544873218055670901
59070627001 * 118141254001 = 6978677948523469881001
59177349001 * 118354698001 = 7003917269513134047001
59236046101 * 118472092201 = 7017818315300358558301
59300079301 * 118600158601 = 7032998810150477217901
59369448601 * 118738897201 = 7049462854314192265801
59406801301 * 118813602601 = 7058336081573583783901
59422809601 * 118845619201 = 7062140601693972748801
59566884301 * 119133768601 = 7096427410597873632901
59833689301 * 119667378601 = 7160140750677370047901[/code]