Reserving the following bases (all new) to n=25K.

Reisel 289

Sierp 259,265,289,317,368

The above bases will all be complete in 4 days. I will report them 1 per day so Gary doesn't kill me.

Are we having fun yet?

I guess I duplicated Sierp Base 300. Nice job Tim. At least we got the same answer. Must have missed your reservation.

Sierp Base 300 officially double-checked. LOL:love:

Primes: (by b then k)
[code]2*269^3+1
2*284^1+1
3*284^1+1
2*299^1+1
2*314^3+1
3*314^280+1
2*329^1+1
2*344^17+1
3*344^1+1
2*359^1+1
2*374^33+1
3*374^1+1
2*389^5+1
2*404^1+1
3*404^1+1
2*419^1+1
2*434^9+1
3*434^1+1
2*449^435+1
2*464^1+1
3*464^2+1
2*479^3+1
2*494^21+1
3*494^1+1
[/code]GFN primes: (by b)
[code]284^2+1
314^2+1
374^4+1
434^8+1
464^2+1
494^4+1
[/code]GFNs with no primes to 32768 (2^15):
[code]344^n+1
404^n+1
[/code]

Riesel Base 289
 

Riesel Base 289
Conjectured k = 86
Covering Set = 5,29
Trivial Factors k == 1 mod 2(2) and 1 mod 3(3)

Found Primes: 27k's File attached

Remaining k's:
36*289^n-1 <----Proven composite by full algebraic factors

Trivial Factor Eliminations: 14k's

Conjecture Proven

HTML attached

Sierp Base 265
 

Sierp Base 265
Conjectured k = 246
Covering Set = 7,19
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 10 mod 11(11)

Found Primes: 74k's File attached

Trivial Factor Eliminations: 48'ks

Conjecture Proven

HTML attached

Almost caught up on my new reservations so:

Reserving Riesel bases 324,441,484
to clean up some k's with full algebraic factors

Riesel Base 324
 

Riesel Base 324
Conjectured k = 14
Covering Set = 5, 13
Trivial Factors k == 1 mod 17(17) and k == 1 mod 19(19)

Found Primes:
2*324^1-1
3*324^1-1
5*324^1-1
6*324^3-1
7*324^1-1
8*324^1-1
10*324^3-1
11*324^149-1
12*324^4-1
13*324^1-1

Remaining k's:
4*324^n-1 <----- Proven composite by full algebraic factors
9*324^n-1 <----- Proven composite by full algebraic factors

Conjecture Proven

HTML attached

Riesel Base 441
 

Riesel Base 441
Conjectured k = 118
Covering Set = 13, 17
Trivial Factors k == 1 mod 2(2) and k == 1 mod 5(5) and k == 1 mod 11(11)

Found Primes: 40k's File attached

Remaining k's:
4*441^n-1 <----- Proven composite by full algebraic factors
64*441^n-1 <----- Proven composite by full algebraic factors

Trivial Factor Eliminations: 16k's

Conjecture Proven

HTML attached

Riesel Base 484
 

Riesel Base 484
Conjectured k = 96
Covering Set = 5, 97
Trivial Factors k == 1 mod 3(3) and k == 1 mod 7(7) and k == 1 mod 23(23)

Found Primes: 49k's File attached

Remaining k's:
9*484^n-1 <----- Proven composite by full algebraic factors
81*484^n-1 <----- Proven composite by full algebraic factors

Trivial Factor Eliminations: 43k's

Conjecture Proven

HTML attached

Sierp Base 259
 

Sierp Base 259
Conjectured k = 144
Covering Set = 5,13
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 42 mod 43(43)

Found Primes: 45k's File attached

Remaining k's: Tested to n=25K
64*259^n+1

Trivial Factor Eliminations: 25k's File attached

Base released

HTML attached

Sierp Base 289
 

Sierp Base 289
Conjectured k = 204
Covering Set = 5,29
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3)

Found Primes: 65k's File attached

Remaining k's: Tested to n=25K
156*289^n+1
160*289^n+1

Trivial Factor Eliminations: 34k's

Base Released

HTML attached

Sierp Base 317
 

Sierp Base 317
Conjectured k = 52
Covering Set = 3, 53
Trivial Factors k == 1 mod 2(2) and k == 78 mod 79(79)

Found Primes: 23k's File attached

Remaining k's: Tested to n=25K
20*317^n+1
44*317^n+1

Releasing Base

HTML attached

Reserving 1 more for algebraic factors.

Riesel 264

[quote=rogue;200662]I found more primes during my PRPNet 3.0 testing.

My apologies if I've stepped on any toes. AFAICT, these were released.

I will continue with them (and a few others) to 25000.[/quote]

No problem. If you have a good idea of which bases you will be running to n=25K and can post them here, I'll go ahead and reserve them for you to avoid any duplication of work.


Gary

[quote=gd_barnes;200767]No problem. If you have a good idea of which bases you will be running to n=25K and can post them here, I'll go ahead and reserve them for you to avoid any duplication of work.

Gary[/quote]

Sierpinski base 353

Sierp Base 368
 

Sierp Base 368
Conjectured k = 40
Covering Set = 3, 41
Trivial Factors k == 366 mod 367(367)

Found Primes: 35k's File attached

Remaining k's: Tested to n=25K
8*368^n+1
12*368^n+1
34*368^n+1

GFN:
k=1 is a GFN with no known prime

Base Released

Riesel Base 264
 

Riesel Base 264
Conjectured k = 54
Covering Set = 5, 53
Trivial Factors k == 1 mod 263(263)

Found Primes: 49k's File attached

Remaining k's:
4*264^n-1 <------ Proven composite by partial algebraic factors
9*264^n-1 <------ Proven composite by partial algebraic factors
49*264^n-1 <------ Proven composite by partial algebraic factors

Conjecture Proven

More algebraic factors

Reserving Riesel 274,294 and 309

Riesel Base 274
 

Riesel Base 274
Conjectured k = 21
Covering Set = 5, 11
Trivial Factors k == 1 mod 3(3) and k == 1 mod 7(7)

Found Primes:
2*274^1-1
3*274^1-1
5*274^4-1
6*274^3-1
11*274^3-1
12*274^51-1
17*274^1-1
18*274^1-1
20*274^1-1

Remaining k's:
9*274^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 9k's

Conjecture Proven

Riesel Base 309
 

Riesel Base 309
Conjectured k = 94
Covering Set = 5, 31
Trivial Factors k == 1 mod 2(2) and k == 1 mod 7(7) and k == 1 mod 11(11)

Found Primes: 35k's File attached

Remaining k's:
4*309^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 10k's

Conjecture Proven

More algebraic factors

Reserving Riesel 324, 334 and 339

[quote=rogue;200769]Sierpinski base 353[/quote]

This is searched to 25K. There are no primes.

I am reserving Riesel and Sierpinski bases 322, 328, and 422.

[QUOTE] More algebraic factors

Reserving Riesel 324, 334 and 339
[/QUOTE]

Oops, 324 already done so I'll do 354 instead along with 334 and 339.

Riesel Base 339
 

Riesel Base 339
Conjectured k = 16
Covering Set = 5, 17
Trivial Factors k == 1 mod 2(2) and k == 1 mod 13(13)

Found Primes:
2*339^1-1
6*339^121-1
8*339^1-1
10*339^1-1
12*339^3-1

Remaining k's:
4*339^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations:
14

Conjecture Proven

More algebraic factors.

Reserving Riesel 364, 369 and 379

If no one objects, I'll be attacking the following base from n=100K to n=200K.

Sierp 252

Riesel Base 294
 

Riesel Base 294
Conjectured k = 119
Covering Set = 5, 59
Trivial Factors k == 1 mod 293(293)

Found Primes: 111k's File attached

Remaining k's: Tested to n=25K
4*294^n-1 <------ Proven composite by partial algebraic factors
6*294^n-1
9*294^n-1 <------ Proven composite by partial algebraic factors
49*294^n-1 <------ Proven composite by partial algebraic factors
64*294^n-1 <------ Proven composite by partial algebraic factors
96*294^n-1

Base Released

Riesel Base 334
 

Riesel Base 334
Conjectured k = 66
Covering Set = 5, 67
Trivial Factors k == 1 mod 3(3) and k == 1 mod 37(37)

Found Primes: 40k's File attached

Remaining k's: Tested to n=25K
9*334^n-1 <------ Proven composite by partial algebraic factors
14*334^n-1

Trivial Factor Eliminations: 22k's

Base Released

Riesel Base 354
 

Riesel Base 354
Conjectured k = 141
Covering Set = 5, 71
Trivial Factors k == 1 mod 353(353)

Found Primes: 132k's File attached

Remaining k's: Tested to n=25K
4*354^n-1 <------ Proven composite by partial algebraic factors
6*354^n-1
9*354^n-1 <------ Proven composite by partial algebraic factors
19*354^n-1
49*354^n-1 <------ Proven composite by partial algebraic factors
64*354^n-1 <------ Proven composite by partial algebraic factors
71*354^n-1

Base Released

Riesel Base 364
 

Riesel Base 364
Conjectured k = 74
Covering Set = 5, 73
Trivial Factors k == 1 mod 3(3) and k == 1 mod 11(11)

Found Primes: 43k's File attached

Remaining k's:
9*364^n-1 <------ Proven composite by partial algebraic factors

Trivial Factors: 28k's

Conjecture Proven

Riesel Base 369
 

Riesel Base 369
Conjectured k = 36
Covering Set = 5, 37
Trivial Factors k == 1 mod 2(2) and k == 1 mod 23(23)

Found Primes: 15k's File attached

Remaining k's:
4*369^n-1 <------ Proven composite by partial algebraic factors

Trivial Factors:
24

Conjecture Proven

Riesel Base 379
 

Riesel Base 379
Conjectured k = 56
Covering Set = 5, 19
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 7(7)

Found Primes: 15k's File attached

Trivial Factor Eliminations: 12k's

Conjecture Proven

Riesel Base 394
 

Riesel Base 394
Conjectured k = 159
Covering Set = 5, 79
Trivial Factors k == 1 mod 3(3) and k == 1 mod 131(131)

Found Primes: 96k's File attached

Remaining k's: Tested to n=25K
9*394^n-1 <------ Proven composite by partial algebraic factors
78*394^n-1
80*394^n-1
81*394^n-1
86*394^n-1
89*394^n-1
144*394^n-1 <------ Proven composite by partial algebraic factors
146*394^n-1

Trivial Factor Eliminations: 53k's

Base Released

Riesel Base 414
 

Riesel Base 414
Conjectured k = 84
Covering Set = 5, 83
Trivial Factors k == 1 mod 7(7) and k == 1 mod 59(59)

Found Primes: 66k's File attached

Remaining k's: Tested to n=25K
4*414^n-1 <------ Proven composite by partial algebraic factors
9*414^n-1 <------ Proven composite by partial algebraic factors
46*414^n-1
49*414^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 12k's

Base Released

Sierp 255
 

Just checking in on my reservation:

I have just crossed the n=24000 mark. Looks like I'm finally reaching the end :smile:

I'm not entirely sure about how many primes i've found since my last update @ n=15000 but I'll count whenever I'm done with the range.
One thing i can tell however is that there will be less than half the original candidates remaining (Currently have 273 candidates remaining out of 547).

[quote=appeldorff;201955]Just checking in on my reservation:

I have just crossed the n=24000 mark. Looks like I'm finally reaching the end :smile:

I'm not entirely sure about how many primes i've found since my last update @ n=15000 but I'll count whenever I'm done with the range.
One thing i can tell however is that there will be less than half the original candidates remaining (Currently have 273 candidates remaining out of 547).[/quote]

An impressive amount of work. Thanks for the update. I'm always personally interested in the 2^q-1 bases so I'll be curious as to what remains when you're through.


Gary

Ian,

In your recent batch, you showed R354 with k=22 & 66 remaining and R394 with k=141 remaining but you also had primes for them in your files so they should have been eliminated.

The error seems to be on primes that were found for n>2500 because your # of found primes was also off by the same amount.

I have corrected the posts. I'll go back and check some previous posts for the same situation.

Edit: I found 2 more back prior to post 900: You showed R294 with k=60 remaining and R334 with k=26 remaining, both of which had primes.

I went all the way back to post 800 and those were the only problems of that nature that I found. It appears that the error just came up more recently where you had bases with more k's remaining in addition to algebraic k's.

Just a heads up...The web pages are now updated to correct the situation.


Gary

[quote]Just a heads up...The web pages are now updated to correct the situation.[/quote]Aha, I found an error in a script I use to shuffle stuff from remaining to prime. Bad testing. Sorry

It's a new script so the damage should just be to those 4 bases.

More algebraic factors

Reserving Riesel base 474

Riesel Base 424
 

Riesel Base 424
Conjectured k = 69
Covering Set = 5, 17
Trivial Factors k == 1 mod 3(3) and k == 1 mod 47(47)

Found Primes: 40k's File attached

Remaining k's: Tested to n=25K
9*424^n-1 <------ Proven composite by partial algebraic factors
18*424^n-1
21*424^n-1
44*424^n-1

Trivial Factor Eliminations: 23k's

Base Released

Riesel Base 429
 

Riesel Base 429
Conjectured k = 44
Covering Set = 5, 43
Trivial Factors k == 1 mod 2(2)

Found Primes: 20k's File attached

Remaining k's:
4*429^n-1 <------ Proven composite by partial algebraic factors

Conjecture Proven

Riesel Base 439
 

Riesel Base 439
Conjectured k = 144
Covering Set = 5, 11
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 73(73)

Found Primes: 42k's File attached

Remaining k's: Tested to n=25K
44*439^n-1
96*439^n-1
120*439^n-1
122*439^n-1

Trivial Factor Eliminations: 25k's

Base Released

Riesel Base 444
 

Riesel Base 444
Conjectured k = 179
Covering Set = 5, 89
Trivial Factors k == 1 mod 443(443)

Found Primes: 163k's File attached

Remaining k's: Tested to n=25K
4*444^n-1 <------ Proven composite by partial algebraic factors
9*444^n-1 <------ Proven composite by partial algebraic factors
11*444^n-1
26*444^n-1
36*444^n-1
49*444^n-1 <------ Proven composite by partial algebraic factors
64*444^n-1 <------ Proven composite by partial algebraic factors
74*444^n-1
96*444^n-1
111*444^n-1
114*444^n-1
123*444^n-1
144*444^n-1 <------ Proven composite by partial algebraic factors
169*444^n-1 <------ Proven composite by partial algebraic factors

Base Released

Riesel Base 459
 

Riesel Base 459
Conjectured k = 24
Covering Set = 5, 23
Trivial Factors k == 1 mod 2(2) and k == 1 mod 229(229)

Found Primes: 10k's File attached

Remaining k's:
4*459^n-1 <------ Proven composite by partial algebraic factors

Conjecture Proven

[QUOTE=MyDogBuster;202010]
4*444^n-1 <------ Proven composite by partial algebraic factors
9*444^n-1 <------ Proven composite by partial algebraic factors
49*444^n-1 <------ Proven composite by partial algebraic factors
64*444^n-1 <------ Proven composite by partial algebraic factors
144*444^n-1 <------ Proven composite by partial algebraic factors
169*444^n-1 <------ Proven composite by partial algebraic factors
[/QUOTE]

I have a question that I hope someone could answer regarding algebraic factorizations. I understand where you can find one (easily) if n is even, but what is the algebraic factorization if n is odd or when n is prime?

[quote=rogue;202017]I have a question that I hope someone could answer regarding algebraic factorizations. I understand where you can find one (easily) if n is even, but what is the algebraic factorization if n is odd or when n is prime?[/quote]
From looking at the lists in the FactorDB, I'm inclined to think the odd n's are eliminated due to a factor of 5. Since I fail to see a mathematical reason for all this, I'll just leave it at that. :smile:

[QUOTE=Mini-Geek;202020]From looking at the lists in the FactorDB, I'm inclined to think the odd n's are eliminated due to a factor of 5. Since I fail to see a mathematical reason for all this, I'll just leave it at that. :smile:[/QUOTE]

But that isn't an algebraic factorization.

[QUOTE=rogue;202022]But that isn't an algebraic factorization.[/QUOTE]

That's why it is a "partial" algebraic factorization, I guess.

[quote=axn;202025]That's why it is a "partial" algebraic factorization, I guess.[/quote]
Yeah, I think the "partial" algebraic factorization covers the even n's, and the factors of 5 (not algebraic factorizations) cover the odd n's.

[QUOTE=Mini-Geek;202026]Yeah, I think the "partial" algebraic factorization covers the even n's, and the factors of 5 (not algebraic factorizations) cover the odd n's.[/QUOTE]

Here is the case. If b%10==4 and n%2==1, then b^n%10==4. Note that when n is odd, that b^n ends with a 4. When n is even b^n ends with a 6. 4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, 4^5 = 1024, etc. If k%10==4 or k%10==9, then k*b^n%10==6, thus k*b^n%5=1, thus (k*b^n-1)%5=0.

Obviously if k is a square and n is even, then k*b^n-1 has the algebraic factorization of sqrt(k)*b^(n/2)-1 * sqrt(k)*b^(n/2)+1.

Gary already shows these on the Riesel Conjectures page.

Would it be helpful for people to list the algrebraic/partial algebraic factorizations when they submit their results?

[quote=rogue;202033]Here is the case. If b%10==4 and n%2==1, then b^n%10==4. Note that when n is odd, that b^n ends with a 4. When n is even b^n ends with a 6. 4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, 4^5 = 1024, etc. If k%10==4 or k%10==9, then k*b^n%10==6, thus k*b^n%5=1, thus (k*b^n-1)%5=0.

Obviously if k is a square and n is even, then k*b^n-1 has the algebraic factorization of sqrt(k)*b^(n/2)-1 * sqrt(k)*b^(n/2)+1.

Gary already shows these on the Riesel Conjectures page.

Would it be helpful for people to list the algrebraic/partial algebraic factorizations when they submit their results?[/quote]

To clarify for the layman: You only gave an example above for b==(4 mod 10). Similar factorizations, only in reverse, can happen where b==(9 mod 10). So technically such factorizations can occur for all b==(4 mod 5).

I feel that this statement:

"Obviously if k is a square and n is even, then k*b^n-1 has the algebraic factorization of sqrt(k)*b^(n/2)-1 * sqrt(k)*b^(n/2)+1."

needs a little clarification to avoid confusion. Yes, all even n are eliminated by algebraic factors when k is squared on the Riesel side. But most of the time, odd n will not have a trivial factor and so the k must still be searched. I wasn't clear if that para. was made in conjunction with the first para.

As an example, the above is why Ian still had to search k=64, 81, 100, etc. on his recently posted base. For bases where b==(4 mod 5), partial algebraic factorizations to make a full covering set can only occur where:

k=m^2 and m==(2 or 3 mod 5)

To be specific, only k=2^2, 3^2, 7^2, 8^2, 12^2, 13^2, etc, or k=4, 9, 49, 64, 144, 169, etc. are partially covered by algebraic factorization to make a full covering set on Ian's base.

Reference wouldn't it be helpful for people to list such factorizations with their results: I think Ian is already showing k's partially covered by algebraic factors to make a full covering set when he submits his primes and k's remaining. I think that works well. Also, whenever someone reserves a base, when putting it on the page, I "usually" state all k's with partial or full algebraic factorizations. Although if it is a large conjecture or a complex situation, I may not "see" them until someone lists their k's remaining at a certain limit.

These get even more involved for bases where b==(12 mod 13), (16 mod 17), (28 mod 29), etc. For more info. see the "generallizing algebraic factors for Riesel bases" thread.

Does anyone have better wording than "covered by partial algebraic factors"? Since we're referring to the entire set of n's on each k here when making that statement, that's what I came up with. Obviously for the even n's, those are covered fully by algebraic factors. But in the universe of n's for those k's, only part of them are covered by algebraic factors.

Perhaps "partially covered by algebraic factors" would be better wording when referring to all n's for each of the covered k's. It's not easy to put it in words clearly.

I figured at some point, the higher math types would come in and pick apart the pages. I'm surprised it's taken this long. I welcome better wording and better ways of showing these "tricky to state" situations where odd n's have a trivial "numeric" factor (factor of 5 in this case) and even n's have "full" algebraic factors.

Axn or Mark, any thoughts about how to more clearly state this mathwise?


Gary

[QUOTE=gd_barnes;202043]
I figured at some point, the higher math types would come in and pick apart the pages. I'm surprised it's taken this long. I welcome better wording and better ways of showing these "tricky to state" situations where odd n's have a trivial "numeric" factor (factor of 5 in this case) and even n's have "full" algebraic factors.

Axn or Mark, any thoughts about how to more clearly state this mathwise?[/QUOTE]

Where Bob Silverman when you need him? :smile:

I agree with everything you have written and no, I can't quickly think of a better way to state it.

[quote=gd_barnes;202043]Perhaps "partially covered by algebraic factors" would be better wording when referring to all n's for each of the covered k's. It's not easy to put it in words clearly.

I figured at some point, the higher math types would come in and pick apart the pages. I'm surprised it's taken this long. I welcome better wording and better ways of showing these "tricky to state" situations where odd n's have a trivial "numeric" factor (factor of 5 in this case) and even n's have "full" algebraic factors.

[B]Axn or Mark[/B], any thoughts about how to more clearly state this mathwise?[/quote]
You may not want me to reply, but I will anyway. :razz:
I'd suggest:
something along the lines of "proven composite by a combination of algebraic and trivial factors" and/or
label it (the thing already listed on every such base explaining this, "All k where k = m^2 ...") Condition 1 (even though it's the only condition for most/all applicable bases) and say "proven composite by condition 1", and/or
instead of listing the Condition on every such base and saying "by condition 1", just link the "proven composite by ..." (or similar) text to somewhere, like an anchor to elsewhere on the page, that has a base-generic form of that statement listed, i.e. one that includes the b==4 mod 5 condition and says b throughout instead of a specific number.

[quote=MyDogBuster;202006]Riesel Base 424
Conjectured k = 69
Covering Set = 5, 17
Trivial Factors k == 1 mod 3(3) and k == 1 mod 47(47)

Found Primes: 40k's File attached

Remaining k's: Tested to n=25K
9*424^n-1 <------ Proven composite by partial algebraic factors
18*424^n-1
21*424^n-1
44*424^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations: 23k's

Base Released[/quote]

k=44 is not eliminated by partial algebraic factors so I'll show it as remaining. Just to confirm: You did test it to n=25K; correct?

[quote=rogue;202017]I have a question that I hope someone could answer regarding algebraic factorizations. I understand where you can find one (easily) if n is even, but what is the algebraic factorization if n is odd or when n is prime?[/quote]

I don't think this ever clearly got answered if someone new just happened to see it. The web pages specify this, although their clarity is probably not the best it could be for many people. This may be beating a dead horse for many of you but I think it needs one final clarification:

Even n's have full algebraic factorization.

Odd n's have a factor of 5. (no algebraic factorization)

This "combines" to what I call "proven composite by partial algebraic factors" to make a full covering set for the entire universe of n-values.

For anyone who hasn't followed the context of the subsequent discussion, this only refers to bases (b) where b==(4 mod 5) and where k=m^2 and m==(2 or 3 mod 5).

To drive the point home just a little more: See Ian's recent work on Riesel base 444. There, k=36 remains whereas k=4, 9, 49, 64, 144, and 169 are eliminated by the above condition. For k=36, although even n have the above algebraic factorization, odd n do not have a trivial factor of 5 so a prime must be found. It just so happens that primes n<25K have already been found for other squares such as k=16, 25, 81, 100, and 121.

FYI, I am mulling over some of the subsequent discussion about rewording the "proven composite by partial algebraic factors". I agree that it should be stated differently but will likely get to it after updating the PFGW new bases script for the latest version of PFGW -and- splitting this thread up into multiple threads like I promised.


Gary

[quote=MyDogBuster;201835]If no one objects, I'll be attacking the following base from n=100K to n=200K.

Sierp 252[/quote]

I now have this officially reserved for you.

[QUOTE]k=44 is not eliminated by partial algebraic factors so I'll show it as remaining. Just to confirm: You did test it to n=25K; correct?[/QUOTE]

Yes, I checked the output, it's tested.

Sierpinski/Riesel Base 322
 

On the Sierpinski side I found:

[code]
3*322^1+1
4*322^1+1
6*322^1+1
7*322^2+1
9*322^2+1
10*322^1+1
12*322^4+1
13*322^2+1
15*322^1+1
16*322^1+1
[/code]

k=1 is a GFN. I didn't do any testing. Are these to be tested separately? The other k have trivial factors.

On the Riesel side I found:

[code]
2*322^1-1
3*322^3-1
5*322^1-1
6*322^1-1
8*322^10-1
9*322^1-1
11*322^1-1
12*322^1-1
14*322^1-1
15*322^2-1
17*322^2-1
[/code]

The other k have trivial factors. This conjecture is proven.

[quote=rogue;202187]On the Sierpinski side I found:

k=1 is a GFN. I didn't do any testing. Are these to be tested separately? The other k have trivial factors.
[/quote]

You can choose to test them or not. I leave it up to the people that start the bases if they want to mess with testing GFNs since it's not necessary to prove or eventually prove the conjectures. If they don't, then I do.

I like to have these mentioned for historical reference only in case there is ever any change to the math that would allow much faster testing for GFNs at high n-limits.

After testing n<=2^15:
322^n+1 is a GFN with no known prime.


Gary

Sierp255
 

And I'm done xD
Sierp 255 is now at n=25000 with 267 k's remaining. Below is a file with all the primes (i sent you the primes up to n=15000 in case you forgot).

I have a zip file with the residues but it's far too big to attach to a forum post. How do you want it? :smile:

EDIT: Sent!

[quote=appeldorff;202270]And I'm done xD
Sierp 255 is now at n=25000 with 267 k's remaining. Below is a file with all the primes (i sent you the primes up to n=15000 in case you forgot).

I have a zip file with the residues but it's far too big to attach to a forum post. How do you want it? :smile:[/quote]

You can Email it to me at:

gbarnes017 at gmail dot com


Thanks! :smile:

[QUOTE=gd_barnes;202271]You can Email it to me at:[/QUOTE]
Do you really collect all these files? Why?

I've got a 30 MB file (5 MB compressed) für sierp b19... :smile:

[quote=Xentar;202281]Do you really collect all these files? Why?

I've got a 30 MB file (5 MB compressed) für sierp b19... :smile:[/quote]

Several reasons:

1. They've helped me detect missed ranges and k's. One that I can specifically remember: One person reported that xx base was complete to n=25K and posted the results. Upon looking in the file, I found that they missed searching one of the k-values.

2. When someone has a typo in a posted prime (I primality test ~half of all primes posted here as a double check), checking the results file for the correct prime saves a lot of time if the person can't mentally remember what the correct one is and it's not an obvious transposition of digits. If the person can't remember the correct one and doesn't have the results, then a lot of CPU time can be wasted double checking the range.

3. Matching up residuals vs. residuals on future double check efforts. Sometimes people might have bad memory (the computer kind, lol) and don't know it. I did one time on a work laptop. This causes bad residuals and hence will miss primes. If we find bad residuals in a particular area of a base, we can know to concentrate more on that area for missed primes and alert the person who searched it.

4. My own comfort level. Some people are extremely detailed and others are not. Some hang around for years and some come-and-go. For the less detailed types and people that come-and-go, it's not uncommon for them to simply miss posting a prime. A review of the results file sets my mind at ease in that regard.

The bottom line is that I try hard to avoid double-work on these bases. I'd hate to search a k up to n=1M and not find a prime and upon a double check, found that it had a prime at n=2000 because someone missed posting it within a myriad of 10's of other small primes. That's why, no matter who it is that starts a new base, I almost always run it up to to n=2500 to check it myself (unless it's a small proven conjecture). That's my small amount of double check to avoid a possible huge future search effort on various k's. On 2-3 occassions that I can recall, I've found primes completely missed by others for n<=2500. It's easy to miss 1-2 of them if you're manually typing them out of a file of 40-50 primes.

The above is why I much prefer that people post actual primes files instead of manually typing them into posts if they have more than ~5-6 primes to post for a base. I've found many many errors in primes manually typed into posts. If it's 1-2 larger primes, then it's no big deal but if it's quite a few smaller primes, posting a file is better. Computers don't transpose digits or mistype a k. :-)

I've had bigger than 5 MB compressed files sent to me, although it's best if they be < 10 MB compressed. (not sure how big google will allow but it's at least that big) If you have time, I'd really appreciate getting your file. What helps me the most is to get them in nice orderly ranges. If you can send me n=25K-30K for Riesel base 19, that'd be great.

That said, the most important results that I like to get are at the very high n-ranges, because there is much greater chance of a bad residual on a long test. (One bad internal calculation for any reason will make it an invalid test.) If you think it's too cumbersome to send me base 19, I'd much prefer to have results on your final k for base 17 (and for some other k's if you can). Those are the ones that we might want to cross-check the residuals on in a future double check effort.

My Email is gbarnes017 at gmail dot com.


Thanks,
Gary

[quote=gd_barnes;202382]I've had bigger than 5 MB compressed files sent to me, although it's best if they be < 10 MB compressed. (not sure how big google will allow but it's at least that big) If you have time, I'd really appreciate getting your file. What helps me the most is to get them in nice orderly ranges. If you can send me n=25K-30K for Riesel base 19, that'd be great.[/quote]
Yeah, I think Gmail's attachment limit is at least 10MB (coming or going), though if the sending account has a smaller limit on outgoing attachments the effective limit would be less. BTW, if anyone has a results file they need to get to Gary that's too big for email, drop me a line ([email]max@noprimeleftbehind.net[/email])--usually I should be able to come up with some way or other to get it where it needs to go. :smile:

Well according to Google Help, the maximum allowed size of an e-mail is: 20MB, so in the case you send an empty e-mail with just 1 attached file, then that file can be 20MB in size, before you send it. So to sum up, the maximum allowed attachement size is:

20MB-the actual size of your written e-mail :smile:

KEP

[quote=KEP;202417]Well according to Google Help, the maximum allowed size of an e-mail is: 20MB, so in the case you send an empty e-mail with just 1 attached file, then that file can be 20MB in size, before you send it. So to sum up, the maximum allowed attachement size is:

20MB-the actual size of your written e-mail :smile:

KEP[/quote]
Keep in mind that attachments must be encoded in base64 before transfer so that they can be packed into an all-ASCII email message; this has the effect of balooning the size a bit. For a huge file, that may add a MB or two.

Riesel Base 474
 

Riesel Base 474
Conjectured k = 39
Covering Set = 5, 19
Trivial Factors k == 1 mod 11(11) and k == 1 mod 43(43)

Found Primes: 32k's File attached

Remaining k's:
4*474^n-1 <------ Proven composite by partial algebraic factors
9*474^n-1 <------ Proven composite by partial algebraic factors

Trivial Factor Eliminations:
12
23
34

Conjecture Proven

[quote=appeldorff;202270]And I'm done xD
Sierp 255 is now at n=25000 with 267 k's remaining. Below is a file with all the primes (i sent you the primes up to n=15000 in case you forgot).

I have a zip file with the residues but it's far too big to attach to a forum post. How do you want it? :smile:

EDIT: Sent![/quote]

Appeldorf,

Per [URL="http://www.mersenneforum.org/showpost.php?p=197457&postcount=48"]this post[/URL] after your n=15K status, k=87036 with a prime at n=4784 was already eliminated. So there are now 266 k's remaining.

Thanks for the large effort! :smile:


Gary

I'm pretty sure i removed k=87036 from my search after you told me. I used a spreadsheet to keep score and i have 267 k's left in that spreadsheet.
But I'll take a look at the k's you list as remaining and see if I forgot to remove one.

ÊDIT: Found it. Forgot to remove k=8956 hehe.

An algebraic straggler.

Reserving Riesel 409.

Riesel Base 409
 

Riesel Base 409
Conjectured k = 534
Covering Set = 5, 41
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 17(17)

Found Primes: 163k's File attached

Remaining k's: Tested to n=25K
144*409^n-1 < Proven composite by partial algebraic factors
284*409^n-1
344*409^n-1

Trivial Factor Eliminations: 100k's

Base Released

Cleaning out the closets now.

Reserving Riesel 476 & 491 and Sierp 491 to n=25K

Sierpinski base 328
 

I have some results to report.

Primes:
[code]
3*328^6+1
4*328^30+1
6*328^7+1
7*328^1+1
9*328^1+1
10*328^3+1
12*328^2+1
13*328^3+1
15*328^2+1
16*328^3+1
18*328^4+1
19*328^3+1
21*328^3+1
22*328^592+1
24*328^1+1
25*328^2+1
28*328^2+1
30*328^201+1
31*328^1+1
33*328^3+1
34*328^13+1
36*328^292+1
37*328^4+1
39*328^2+1
40*328^1+1
42*328^4+1
43*328^2+1
45*328^19+1
46*328^3+1
[/code]

Trivially factored
[code]
2
5
8
11
14
17
20
23
26
29
32
35
38
41
44
47
[/code]


I have not tested GFNs, i.e. k=1.

The only remaining k without a prime is 27. I have tested it to 25K. I am releasing this base.

Riesel Base 328
 

I have some results to report.

Primes:
[code]
2*328^80-1
3*328^1-1
5*328^2-1
6*328^2-1
9*328^605-1
11*328^1-1
12*328^2-1
14*328^1-1
15*328^1-1
17*328^3-1
18*328^1-1
20*328^20962-1
21*328^3-1
23*328^2-1
24*328^4-1
26*328^1-1
27*328^2-1
29*328^1-1
30*328^1-1
32*328^22-1
33*328^2-1
35*328^6603-1
36*328^1-1
38*328^2-1
39*328^1-1
42*328^447-1
44*328^1-1
45*328^1-1
47*328^3-1[/code]

Trivially factored
[code]
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46[/code]


The remaining k without a prime are 8 and 41. I have tested it to 25K. I am releasing this base.

Riesel Base 476
 

Riesel Base 476
Conjectured k = 52
Covering Set = 3, 53
Trivial Factors k == 1 mod 5(5) and k == 1 mod 19(19)

Found Primes: 37k's File attached

Remaining k's: Tested to n=25K
49*476^n-1

Trivial Factor Eliminations: 12k's

Base Released

Riesel Base 491
 

Riesel Base 491
Conjectured k = 40
Covering Set = 3, 41
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 mod 7(7)

Found Primes: 13k's File attached

Trivial Factor Eliminations: 6k's

Conjecture Proven

Sierp Base 491
 

Sierp Base 491
Conjectured k = 40
Covering Set = 3, 41
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 6 mod 7(7)

Found Primes: 13k's File attached

Trivial Factor Eliminations: 6k's

Conjecture Proven

Reserving R257...

Proven with a highest prime of 42*257^58-1.

:smile:

To test the latest new-bases script, I decided to take a whack at a few of the lowest untested Sierpinski conjectures. Here's my results:

Sierp. base 279: conjectured k 6, proven, primes:
2*279^4+1
4*279^1+1

Sierp. base 349: conjectured k 6, proven, primes:
4*349^3+1
k=2 was eliminated by trivial factors.

Sierp. base 384: conjectured k 6, proven, primes:
2*384^1+1
3*384^1+1
4*384^21+1
5*384^2+1
k=1 is a GFN.

Sierp. base 454: conjectured k 6, proven, primes:
3*454^2+1
4*454^3+1
k=2 and k=5 eliminated by trivial factors; k=1 is a GFN.

Sierp. base 489: conjectured k 6, proven, primes:
2*489^2+1
4*489^5+1

That's all for now...don't want to inundate Gary with too many of these. :wink:

That's cool Max. I had thought of doing a few k=6 conjectures also previously.

I was asking for parallel testing. These are brand new bases so there was nothing to parallel with. I'm sure they are correct but I just wanted to point out the difference between new testing and parallel testing.

It's best to test new and changed software with "test data" not "production data". Running new bases with newly changed software means you have "tested" it in "production", which is not a good idea.

If you'd like to help me out here, how about running the previous version of the script against these bases also and see if you get the same results? Then we'll have a true parallel test.

[quote=gd_barnes;205300]That's cool Max. I had thought of doing a few k=6 conjectures also previously.

I was asking for parallel testing. These are brand new bases so there was nothing to parallel with. I'm sure they are correct but I just wanted to point out the difference between new testing and parallel testing.

It's best to test new and changed software with "test data" not "production data". Running new bases with newly changed software means you have "tested" it in "production", which is not a good idea.

If you'd like to help me out here, how about running the previous version of the script against these bases also and see if you get the same results? Then we'll have a true parallel test.[/quote]
Sure. I don't have the version 4.2 script; could you send that one to me? (Unless you meant for me to test it with 4.1? I'd have to dig up an older version of PFGW, but I could do it if you'd like.)

[quote=mdettweiler;205304]Sure. I don't have the version 4.2 script; could you send that one to me? (Unless you meant for me to test it with 4.1? I'd have to dig up an older version of PFGW, but I could do it if you'd like.)[/quote]

Yeah, use 4.1 if you can find PFGW 3.2.3 or earlier. That would be a good parallel test. It should still write out the appropriate GFNs. It wouldn't have the compPRP and PRP files but I seriously doubt that those will apply for such small conjectured bases.

[quote=gd_barnes;205306]Yeah, use 4.1 if you can find PFGW 3.2.3 or earlier. That would be a good parallel test. It should still write out the appropriate GFNs. It wouldn't have the compPRP and PRP files but I seriously doubt that those will apply for such small conjectured bases.[/quote]
Hmm...I'm having a hard time locating a copy of 3.2.3 (I think the binaries may have been taken offline), though I do have a really old copy sitting around (the latest of the "old" versions, i.e. pre-3.0). The speed differences shouldn't be an issue for numbers this small; should the script be compatible with that version? (As I recall, no changes were made in the area of scripts until 3.2.5 or so, but I could be wrong.)

[quote=mdettweiler;205309]Hmm...I'm having a hard time locating a copy of 3.2.3 (I think the binaries may have been taken offline), though I do have a really old copy sitting around (the latest of the "old" versions, i.e. pre-3.0). The speed differences shouldn't be an issue for numbers this small; should the script be compatible with that version? (As I recall, no changes were made in the area of scripts until 3.2.5 or so, but I could be wrong.)[/quote]

As far as I know, that should work. The first good release that the new script changes worked with is 3.2.7. The last for version 4.1 of the script is 3.2.3.

[quote=gd_barnes;205310]As far as I know, that should work. The first good release that the new script changes worked with is 3.2.7. The last for version 4.1 of the script is 3.2.3.[/quote]
Okay, here's what I got:

Sierp. base 279: same output in the files, but I'm not positive if it actually proved the PRP for 2*279^4+1. Here's the console output:
[code]PFGW Version 1.2.0 for Windows [FFT v23.8]
Factoring numbers to 30% of normal.
Script File
2*279^1+1 trivially factors as: 13*43
2*279^2+1 trivially factors as: 11*14153
2*279^3+1 trivially factors as: 113*384383
trial factoring to 19660
Switching to Exponentiating using GMP
2*279^4+1 is 3-PRP! (0.0000s+0.0081s)
4*279^1+1 trivially factors prime!: 1117[/code]
2*279^4+1 shows up in pl_prime.txt, however, so if the script did prove it, it just didn't say so on the screen.

Sierp. base 349: same as before

Sierp. base 384: similar to what happened with S279. 4*384^21+1 was shown as 3-PRP on screen, and was listed in pl_prime.txt, but I didn't see proof of a proof (no pun intended) on screen.

Sierp. base 454: same as before

Sierp. base 489: similar to S279 and S384. 4*489^5+1 was shown as 3-PRP on screen and listed in pl_prime.txt, but not shown on screen as N-1'ed or factored prime.

Note that, in all the cases where the 4.1 script neglected to log a proof to the screen, the 4.3 script quite clearly showed that it proved the primes in one way or another after having initially found them 3-PRP.

At any rate, the results seem to be resoundingly good for 4.3: the only potential problems I turned up were in 4.1, and were for issues which I believe were the primary issues addressed in 4.3, which handled them exactly as it should. :smile:

[quote=mdettweiler;205316]Okay, here's what I got:

Sierp. base 279: same output in the files, but I'm not positive if it actually proved the PRP for 2*279^4+1. Here's the console output:
[code]PFGW Version 1.2.0 for Windows [FFT v23.8]
Factoring numbers to 30% of normal.
Script File
2*279^1+1 trivially factors as: 13*43
2*279^2+1 trivially factors as: 11*14153
2*279^3+1 trivially factors as: 113*384383
trial factoring to 19660
Switching to Exponentiating using GMP
2*279^4+1 is 3-PRP! (0.0000s+0.0081s)
4*279^1+1 trivially factors prime!: 1117[/code]
2*279^4+1 shows up in pl_prime.txt, however, so if the script did prove it, it just didn't say so on the screen.

Sierp. base 349: same as before

Sierp. base 384: similar to what happened with S279. 4*384^21+1 was shown as 3-PRP on screen, and was listed in pl_prime.txt, but I didn't see proof of a proof (no pun intended) on screen.

Sierp. base 454: same as before

Sierp. base 489: similar to S279 and S384. 4*489^5+1 was shown as 3-PRP on screen and listed in pl_prime.txt, but not shown on screen as N-1'ed or factored prime.

Note that, in all the cases where the 4.1 script neglected to log a proof to the screen, the 4.3 script quite clearly showed that it proved the primes in one way or another after having initially found them 3-PRP.

At any rate, the results seem to be resoundingly good for 4.3: the only potential problems I turned up were in 4.1, and were for issues which I believe were the primary issues addressed in 4.3, which handled them exactly as it should. :smile:[/quote]


There were no issues in 4.1. 4.3 only resolved extremely rare issues in 4.2. At the time of 4.1, the scripting language had no way to prove PRPs so 4.1 did all that it could and assume that PRPs were prime and left it up to the user to prove them.

There is nothing extraordinary about 4.3 by any means. The changes that you're observing with the proof of the PRPs started with 4.2 and PFGW 3.2.7. 4.2 has been around for several weeks now.

All that 4.3 did is resolve issues in extremely rare situations where a PRP came through the PRIMEM/PRIMEP primality proof as STILL PRP and on even more rare situations where it came through as a composite PRP yet really wasn't composite and factoring and or combined testing with PRIMEC could find it to be prime.

I'm certain that none of the very rare situations that 4.3 resolved cropped up in your testing here (hence why nothing extraordinary). I had to actually change the max factoring to a lower limit while testing 4.3 just to get some of the situations to hit such rare conditions in base 3.

The main thing that I wanted to verify is that the GFN, MOB, primes, and k's remaining files are all the same. Since there are no MOB or k's remaining for these bases, more parallel testing is needed.

BTW, screen output, the pfgw.log file, and the pfgw-prime.log file are useless when running the script. (Sometimes the pfgw.out file can be used for debugging certain situations.) Only the pl_ prefix files are applicable. If you come across a MOB, you'll see extra primes coming through those pfgw.log and pfgw-prime.log files, which don't pertain to the conjecture, hence they should just be deleted when you are through.

I have to admit, it's fun being the programmer doing the testing and debugging for a change. :-)


Gary

Ah, okay, that makes sense. I figured the screen output was somewhat irrelevant, but nonetheless thought it worth mentioning, just in case.

BTW, for future parallel testing, is it worth doing that by comparing 4.1/4.3 as I did here, or would it really need to be 4.2/4.3 in order to be useful?

[quote=mdettweiler;205325]Ah, okay, that makes sense. I figured the screen output was somewhat irrelevant, but nonetheless thought it worth mentioning, just in case.

BTW, for future parallel testing, is it worth doing that by comparing 4.1/4.3 as I did here, or would it really need to be 4.2/4.3 in order to be useful?[/quote]

4.1 vs. 4.3 is just as relevant.

Please keep in mind to run already tested bases first, else you're "testing" in "production". For example, take both sides of bases 512 or 1024 and run them in 4.1 and then again in 4.3 to see if the files match.

After several previously tested bases come back as in sync, then you can run some new bases. The point of parallel testing is to verify that changes to existing software have not adversely affected what the prior software has already come up with. Once that is done, the new software can be rolled out on new data or as is the case here, new bases.

In other words, I would classify this as a late stage beta test.


Gary

Riesel Base 288
 

Reserving Riesel base 288 as new to n=25K

Riesel Base 288
 

Riesel Base 288
Conjectured k = 613
Covering Set = 5, 17, 53
Trivial Factors k == 1 mod 7(7) and k == 1 mod 41(41)

Found Primes: 505k's File attached

Remaining k's: 6k's Tested to n=25K
16*288^n-1 <---------- Proven composite by partial algebraic factors
18*288^n-1
339*288^n-1
392*288^n-1
441*288^n-1 <---------- Proven composite by partial algebraic factors
509*288^n-1

Trivial Factor Eliminations: 99k's

MOB Eliminations:
576

Base Released

Reserving R251.

Riesel base 251, conjectured k = 8, proven
Primes:
2*251^2-1
4*251^271-1

k=6 removed by trivial factors
k=8 is proven composite (all numbers are divisible by 3 or 7)

Sierpinski base 422
 

Primes found:

[code]
2*422^3+1
3*422^2+1
4*422^2634+1
5*422^1+1
6*422^32+1
7*422^2+1
9*422^105+1
10*422^2978+1
11*422^1+1
12*422^394+1
14*422^5+1
15*422^12+1
18*422^13+1
19*422^7302+1
20*422^355+1
21*422^1+1
23*422^989+1
24*422^3+1
25*422^4+1
26*422^1+1
27*422^2+1
28*422^2+1
29*422^1+1
30*422^2+1
32*422^179+1
32*422^179+1
33*422^1302+1
34*422^946+1
35*422^1+1
36*422^1+1
37*422^13020+1
38*422^45+1
39*422^5+1
40*422^286+1
41*422^4319+1
42*422^4+1
43*422^2+1
44*422^223+1
45*422^3+1
[/code]

Remaining k at n=25000:
[code]
8*422^n+1
13*422^n+1
16*422^n+1
17*422^n+1
22*422^n+1
31*422^n+1
[/code]

I am releasing this base. This is just a nasty base because a large percentage of k remain. Does anyone know which conjectures (to this point) have the largest ratio of k remaining to conjectured k?

Riesel base 321 (conjectured k=22)
Primes:
2*321^1-1
4*321^1-1
10*321^1-1
12*321^1-1
14*321^1-1
18*321^4-1
20*321^1406-1

k=6 and k=16 removed by trivial factors.

Remaining k=8 tested to 25K with no primes, I'll reserve it to 100K.

[quote=unconnected;206059]Remaining k=8 tested to 25K with no primes, I'll reserve it to 100K.[/quote]
All n == 0 mod 3 can be eliminated since 8 is a cube.

[tex]8*321^n-1=2^3*321^{3m}-1=(2*321^m)^3-1[/tex]
And a sum or difference of cubes (1 is also a cube) has algebraic factors: [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

This eliminated ~100 candidates after sieving to 10G, not so bad. I wrote bash-script to do this, is there an easier way?

[quote=unconnected;206102]This eliminated ~100 candidates after sieving to 10G, not so bad. I wrote bash-script to do this, is there an easier way?[/quote]
Well, I made this Perl script a while ago: [url]http://www.mersenneforum.org/showthread.php?p=199328#post199328[/url]
It's probably a bit more complex and flexible (and so harder to use) than you need, but it works. :smile: