Reserving the following bases from my former k=2 search. I had already done some work on all of them to n=5K or 10K and have recently been moving them up towards n=25K. I'll post a status separately.

R383
S365
S461
S467

S461 is complete to n=25K; only k=2 remains; base released.
S467 is complete to n=25K; k=2 & 4 remain; base released.

Riesel Base 422
 

Primes found:

[code]
2*422^540-1
3*422^190-1
4*422^21737-1
5*422^2-1
6*422^1-1
7*422^1-1
8*422^2944-1
9*422^1-1
10*422^1-1
12*422^8-1
15*422^1-1
16*422^247-1
17*422^6-1
18*422^11-1
19*422^1-1
20*422^6-1
21*422^1-1
22*422^1-1
23*422^5568-1
24*422^4-1
25*422^9-1
26*422^642-1
27*422^1-1
28*422^3-1
30*422^1-1
31*422^33-1
32*422^6-1
33*422^11-1
34*422^1-1
35*422^2-1
36*422^37-1
38*422^2-1
39*422^21-1
40*422^1-1
41*422^22802-1
42*422^48-1
43*422^11-1
44*422^4-1
45*422^43-1
[/code]

k=1 has trivial factors.

These k remain:

[code]
11*422^n-1
13*422^n-1
14*422^n-1
29*422^n-1
37*422^n-1
[/code]

I have tested to n=25000 and am releasing the base.

S365 is complete to n=25K; k=2 & 176 remain; base released.

R383 is complete to n=25K; 2 primes found for n=5K-25K; 9 k's remaining; base released.

Since this was from my original k=2 search effort and despite only eliminating 2 out of 11 k's after n=5K, I was lucky enough to find:
2*383^20956-1 is prime!

This leaves Riesel bases 170 and 303 as the only 2 bases < 500 where k=2 does not yet have a prime on the Riesel side. R170 is at n=50K and shown on the pages and R303 is at n=10K and not shown. As a base, R303 is a tough one due to its high conjecture of k=85368, although I may search just k=2 for it up to n=25K in the near future.

The Sierp side still has 7 bases < 500 remaining where k=2 does not yet have a prime. 6 out of 7 have been searched to n>=25K with base 383 as the only one not yet there at n=10K. With a conjecture of k=1022, it doesn't appear bad but a prelimiary search to n=2500 showed 64 k's remaining so I haven't been willing to take it on just yet.

One more note of interest on the k=2 search effort: Base 383 had been the lowest base where k=2 remained on both sides. Now the lowest is base 578. k=2 on both sides has been searched to n=10K. Despite low conjectures on both sides, the base is remarkably low weight and hence there are 23 and 10 k's remaining respectfully at n=2500.


Gary

Taking Sierpinski base 484 with conjectured k = 96.

Sierpinski base 484
 

Primes Found:

[code]
3*484^1+1
4*484^3+1
7*484^1+1
9*484^1+1
10*484^16+1
12*484^2+1
15*484^57+1
16*484^10+1
18*484^1+1
19*484^5+1
21*484^1060+1
24*484^1+1
25*484^1+1
28*484^1+1
30*484^41+1
31*484^8+1
33*484^1+1
36*484^204+1
37*484^1+1
39*484^33+1
40*484^3+1
42*484^6+1
43*484^2+1
46*484^2+1
49*484^3+1
51*484^4+1
52*484^1+1
57*484^8+1
58*484^6+1
60*484^8+1
61*484^10+1
63*484^1+1
64*484^1+1
66*484^24+1
67*484^1+1
70*484^10+1
72*484^1+1
73*484^4+1
75*484^4+1
78*484^864+1
79*484^1+1
81*484^16+1
82*484^2+1
84*484^103+1
85*484^1+1
87*484^12+1
88*484^27+1
93*484^1+1
94*484^1+1
[/code]

k=1 is a GFN. I have not tested it.

k=54 remains and has been tested to n=25000.

The other k have trivial factors.

I will continue to work on this conjecture. Maybe I'll get lucky and knock off another conjecture that has a single k remaining.

Reserving R328 to 100K

R321 complete to 100K, releasing base.

[quote=Batalov;207606]Reserving R328 to 100K[/quote]
Now, 41*328^31734-1 showed up prime and promoted R328 to the one-k club. Going on...

Reserving Riesel Bases 469 and 499 as new to n=25K.

R294 is proven (with a pencil)
 

b=294=6*7[sup]2[/sup]

k=6: for even n, divisible by 5; for odd n=2m-1,
6*294[sup]2m-1[/sup]-1 = 6*(6*7^2)[sup]2m-1[/sup]-1 = 6[sup]2m[/sup] * 7[sup]2n[/sup] - 1[sup]2[/sup] = Difference of squares.

k=96=6*4[sup]2[/sup]: ditto.

qed :smile:

R288
 

[I]b[/I]=288 = [B]2[/B][sup][B]5[/B][/sup]*3[sup]2[/sup]
[I]k[/I]=18 = [B]2[/B]*3[sup]2[/sup]
[I]k[/I]=392 = [B]2[/B][sup][B]3[/B][/sup]*7[sup]2[/sup]
For both [I]k[/I] and even [I]n[/I], trivial factors, for odd [I]n[/I], we have differences of squares.

Reserving to 50K (two k remaining).

R444, [I]k[/I]=111 eliminates (algebraic with [I]n[/I] odd, trivial with even)...

There's probably quite a few more of these.

One last proof before going to sleep:

R414 is proven (k=46 = b/3[SUP]2[/SUP]); the rest is ditto.

Maybe Gary or someone else has the answer to this one. I have 54*484^n+1 reserved. Clearly 484 = 22^2. A prime was found for 54*22^n+1, but I don't know what n it was prime for. If n was even then that would prove Sierpinski base 484.

[quote=rogue;208048]Maybe Gary or someone else has the answer to this one. I have 54*484^n+1 reserved. Clearly 484 = 22^2. A prime was found for 54*22^n+1, but I don't know what n it was prime for. If n was even then that would prove Sierpinski base 484.[/quote]
These are the primes for that base 22 k with n<=1000:
54*22^13+1 is 3-PRP! (0.0000s+0.0006s)
54*22^39+1 is 3-PRP! (0.0001s+0.0011s)
Both odd n.
It was eliminated so early that it's of no real value in the search for a 54*484^n+1 prime. If it had a prime with an even n, base 484 would have the same prime at half the n.

[quote=Batalov;208046]One last proof before going to sleep:

R414 is proven (k=46 = b/3[sup]2[/sup]); the rest is ditto.[/quote]
I was too sleepy last night, so I didn't elaborate. I will use this space to generalize.

Let b=k*x^2 and n=2m-1 is odd. Then
k*b[sup]2m-1[/sup]-1 = k*(k*x^2)[sup]2m-1[/sup]-1 = k[sup]2m[/sup]x[sup]2n[/sup] - 1[sup]2[/sup] = (k[sup]m[/sup]x[sup]n[/sup] - 1)(k[sup]m[/sup]x[sup]n[/sup] + 1), and is composite.
For the even n's, if there's a trivial factor (which is to be found case by case, using a hint from the srsieve and then doing modular arithmetics in mod 5, or mod 17, or mod N to be found), then the k is eliminated.

Here, b=414, x=3 (and k=46). And for even n, k*b[sup]2m[/sup]-1 [FONT=Times New Roman]≡[/FONT] 1*(-1)[sup]2m[/sup]-1 [FONT=Times New Roman]≡[/FONT] 0 (mod 5)

Other cases were ([I]may be typos here[/I]):
b=444, x=2
b=288, x=4 and "7/6" {x=7,y=6} (a variation to the above proof: 288=2^5*3^2, 392=2^3*7^2)
b=294, x=7 and "7/2" {x=7,y=2}
b=864, x=3 and x=12

Similar for k=b*x^2 (a special case of a multiple of base): left as an excercise.

In all cases, one thing is common: [B]k*b is a square[/B].
Ah, where were my eyes. :-) The whole thing is so easily re-written now:
Let k*b be a square, then for odd n's we trivially observe the difference of squares.
But I'll leave the blueprints. Could be educational. Sometimes such a simple idea comes only after a scribbled list... well, you know. Fun, fun.

Now, if [B]k*b^2 or k*b is a cube[/B], one obtains algebraics for both Riesel and Sierp for certain n's; similar (but rarer) for fifth degrees, etc.

Look for such cases in your bases.
__________

Now I'd like to get back to the earlier argument: should the sieve [I]or[/I] pfgw remove such cases by a fast factorization of [I]k[/I] and [I]b[/I]?
I think, both!
Or [I]the script[/I].
This is because when people start a new base, they initially use pfgw and [I]the script[/I]. They don't even get to the srsieve until much later.

[QUOTE=Mini-Geek;208050]These are the primes for that base 22 k with n<=1000:
54*22^13+1 is 3-PRP! (0.0000s+0.0006s)
54*22^39+1 is 3-PRP! (0.0001s+0.0011s)
Both odd n.
It was eliminated so early that it's of no real value in the search for a 54*484^n+1 prime. If it had a prime with an even n, base 484 would have the same prime at half the n.[/QUOTE]

I've searched up to n=~65000 for this with no luck yet. Considering how heavy this k/b combo is (>4.5% tests remain after sieving), I was hoping for a quick knock out.

Sierp 275, 281 & 307
 

Reserving Sierp 275, 281, 307 and 338 as new to n=25K

R405 is proven
 

R405 is proven with conj. k=146.
Data is attached.

Reserving as new S405 and R/S441.

54*484^69515+1 is prime.

At 186,639 digits, this will make it into the Prime Pages.

And t also proves the Sierpinski conjecture for base 484.

And it also removes a rather nasty conjecture with a single k remaining.

54*484^69515+1 is prime!

Riesel Base 285
 

2*285^1-1
4*285^71-1
6*285^1-1
8*285^2-1
10*285^2-1

With a conjectured k of 12, this conjecture is proven.

[quote=rogue;208443]54*484^69515+1 is prime![/quote]

Nice proof Mark. I wondered what that Sierp base 22 prime was that came across on top 5000. :smile:

R252 is proven

[URL="http://www.mersenneforum.org/posthistory.php?p=208595"][I][COLOR=seagreen]Last fiddled with by Batalov[/COLOR][/I][/URL][I][COLOR=seagreen]; 16 Mar 10 at 10:32 PM Reason: I thought this thread was "up to 256"; please move to 251+[/COLOR][/I]
[I][COLOR=#2e8b57][B]mdettweiler: [/B]moved[/COLOR][/I]

R441, S441, R472 are proven
 

R441, S441, R472 are proven.
To save space, all three in one zip.

S405 is reserved. One k=106 remains.
Reserving R450 as new. One k=57 remains.
Data is attached.

Nice work everyone in figuring out those k's with algebraic factors to make a full covering set on various bases.

It's definitely a big "hole" in the pages right now that I'll be looking at over the next 1-2 days.

That's interesting that the "new" kind of algebraic factors are always k*b = a perfect square.

Willem, your analogy on R40 looks correct. I only checked the k's that you found that could be eliminated and no others.

Edit: I've now checked all k's on the base. Nothing else found.

R361
 

Reserving R361 with conjectured k=8870 as new to 25K.
At n=1500, there are only 45 [I]k[/I]'s left. 44... 43...
Initial files are attached.
[SIZE=1](Two R19 primes are included; they were the smallest for R19, so they are the smallest for R361 as well.)[/SIZE]
________

Gary, if you have all R19 primes, could please PM?
Of interest are somewhat larger even [I]n[/I]'s, except for two odd [I]n[/I]'s for k=138 and [strike]366[/strike]. The small primes of course will be soon rediscovered anyway.

[quote=Batalov;208042]b=294=6*7[sup]2[/sup]

k=6: for even n, divisible by 5; for odd n=2m-1,
6*294[sup]2m-1[/sup]-1 = 6*(6*7^2)[sup]2m-1[/sup]-1 = 6[sup]2m[/sup] * 7[sup]2n[/sup] - 1[sup]2[/sup] = Difference of squares.

k=96=6*4[sup]2[/sup]: ditto.

qed :smile:[/quote]

Stop those pencil proofs! lol :smile:

Good work as usual.

[quote=Batalov;208082]
Now I'd like to get back to the earlier argument: should the sieve [I]or[/I] pfgw remove such cases by a fast factorization of [I]k[/I] and [I]b[/I]?
I think, both!
Or [I]the script[/I].
This is because when people start a new base, they initially use pfgw and [I]the script[/I]. They don't even get to the srsieve until much later.[/quote]

IMHO, it should be in the sieving software. After all, sieving software is for finding factors. To "generalize" its use further, it should find both "numeric" and algebraic factors as best as it can. Similarly, primality proof software is for proving primes, not finding factors.

PFGW as a primality proof program really does us a kindness by having a trial factoring option but that is only a "nicety" option that avoids the extra effort of sieving teeny n-ranges. IMHO, it's usefulness would be virtually as good without such an option.

Even if the sieving software only found "very simple" algebraic factors such as where k and b are both a perfect square/cube/5th power/etc., then its usefulness would be increased. From there, you could then expand its usefullness by having it find "somewhat simple" algebraic factors as shown in the "Generalizing algebraic factors for Riesel bases thread" followed by the "medium difficulty" algebraic factors as you guys have recently found for odd n's where k*b is a square, and then finally finding algebraic factors for cubes and higher powers where there is no very simple pattern and where k and/or b are not necessarily perfect powers of any kind.

All of this said, my/our starting bases script should also be able to eliminate k's with partial algebraic factors to make a full covering set. Why? Because we don't sieve when starting new bases. We (at least me anyway) only do trial factoring to 100% using the -f switch. It is something on the backburner in my head and will be a fairly major enhancement. I will likely start the process as shown above by doing the easy ones where both k and b are perfect squares/cubes/high powers first as a new version 5.0. From there, I'll add them as shown above for versions 5.1, 5.2, etc. Likely I won't do the final one because the situations in which they will apply to this project will be quite rare.


Gary

...I have already started groking the sr(x)sieve code to make some insightful (as usual) additions... :rolleyes:

I always use srsieve to "confirm" (empirically, of course) the conjectured [I]k[/I] -- I set max_k to the conjectured[I] k[/I] and it stays in the pl_remain.txt and is then fed to the srsieve, which in turn doesn't even produce an .npg file with the message that all candidates were eliminated. After the patch, it will do that for some other (partial-trivial+algebraic) [I]k[/I]'s as well; it will also make smaller .npg files in the partial-but-not-complemented-by-trivial algebraic cases.
Which, I think, will be the desired behaviour.
___________

[COLOR=green]R361 is down to only 24 [I]k[/I]'s (at n~=15K in terms of base-19) and may shed some more if you will find some R19 primes from the archives? /wink-wink-nudge-nudge/[/COLOR]

[QUOTE=Batalov;208853]...I have already started groking the sr(x)sieve code to make some insightful (as usual) additions... :rolleyes:

I always use srsieve to "confirm" (empirically, of course) the conjectured [I]k[/I] -- I set max_k to the conjectured[I] k[/I] and it stays in the pl_remain.txt and is then fed to the srsieve, which in turn doesn't even produce an .npg file with the message that all candidates were eliminated. After the patch, it will do that for some other (partial-trivial+algebraic) [I]k[/I]'s as well; it will also make smaller .npg files in the partial-but-not-complemented-by-trivial algebraic cases.
Which, I think, will be the desired behaviour.
___________

[COLOR=green]R361 is down to only 24 [I]k[/I]'s (at n~=15K in terms of base-19) and may shed some more if you will find some R19 primes from the archives? /wink-wink-nudge-nudge/[/COLOR][/QUOTE]

I suggest that you give those changes to Geoff Reynolds. I know that he is very busy, but I suspect that he would welcome the input.

Of course.

[quote=Batalov;208603]S405 is reserved. One k=106 remains.
Reserving R450 as new. One k=57 remains.
Data is attached.[/quote]

I need a search limit on these. Also, is R450 still reserved?

One more thing: Can you please slow down on the new bases for a few days? I need to catch my breath. We have so much work to do on bases that have already been started.

[quote=Batalov;208733]Reserving R361 with conjectured k=8870 as new to 25K.
At n=1500, there are only 45 [I]k[/I]'s left. 44... 43...
Initial files are attached.
[SIZE=1](Two R19 primes are included; they were the smallest for R19, so they are the smallest for R361 as well.)[/SIZE]
________

Gary, if you have all R19 primes, could please PM?
Of interest are somewhat larger even [I]n[/I]'s, except for two odd [I]n[/I]'s for k=138 and [strike]366[/strike]. The small primes of course will be soon rediscovered anyway.[/quote]

Here are n=2K to 30K attached. See the pages for the top 10, which include higher primes. k<10K was searched to n>=100K. See the base 19 reservations page for the exact search depths.

I'll post an update on the pages when you're at n>=10K for all k's.


Gary

Thank you for the R19 results.

For any reservations with unspecified limits, I expect to deliver towards the unwritten default of 25K.

Sierp Base 275
 

Sierp Base 275
Conjectured k = 22
Covering Set = 3, 23
Trivial Factors k == 1 mod 2(2) and k == 136 mod 137(137)

Found Primes:
2*275^3+1
4*275^158+1
6*275^4+1
8*275^19+1
10*275^2+1
12*275^1+1
14*275^1+1
16*275^4+1
18*275^1+1
20*275^1+1

Conjecture Proven

Sierp Base 281
 

Sierp Base 281
Conjectured k = 46
Covering Set = 3, 47
Trivial Factors k == 1 mod 2(2) and k == 4 mod 5(5) and k == 6 mod 7(7)

Found Primes:
2*281^1+1
8*281^1843+1
10*281^2+1
12*281^1+1
16*281^2+1
18*281^1+1
22*281^6+1
26*281^1+1
28*281^46+1
30*281^1+1
32*281^63+1
36*281^2+1
38*281^7+1
40*281^36+1
42*281^2+1

Trivial Factor Eliminations:
4
6
14
20
24
34
44

Conjecture Proven

Sierp Base 307
 

Sierp Base 307
Conjectured k = 34
Covering Set = 7, 11
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 16 mod 17(17)

Found Primes:
4*307^1+1
6*307^549+1
10*307^3423+1
12*307^490+1
18*307^1+1
22*307^24+1
24*307^1+1
28*307^1+1
30*307^4+1

Trivial Factor Eliminations:
2
8
14
16
20
26
32

Conjecture Proven

Oh boy, 2 new bases a day we get. I'll probably be doing about 2 a week. I'm in the process of returning to NPLB for their new k=301-399 n=1M-2M drive with about 16 cores.

Reserving R304 and S319 as new to n=25K.

[quote=MyDogBuster;209325]Oh boy, 2 new bases a day we get. I'll probably be doing about 2 a week. I'm in the process of returning to NPLB for their new k=301-399 n=1M-2M drive with about 16 cores.

Reserving R304 and S319 as new to n=25K.[/quote]

Do I sense a hint of sarcasm there? lol :smile:

Oops, I accidentally did three bases. :redface:

R265 is proven (c.k=20):
[CODE]2*265^2-1
6*265^2-1
8*265^71-1
14*265^1-1
18*265^2-1
4 - trivials
10
12
16[/CODE]

Riesel Base 304
 

Riesel Base 304
Conjectured k = 426
Covering Set = 5, 61
Trivial Factors k == 1 mod 3(3) and k == 1 mod 101(101)

Found Primes: 268k's - File attached

Remaining: 8k's - Tested to n=25K
131*304^n-1
284*304^n-1
294*304^n-1
339*304^n-1
374*304^n-1
389*304^n-1
404*304^n-1
411*304^n-1

k=9, 144, 324 proven composite by partial algebraic factors
k=171 proven composite by a difference of squares

Trivial Factor Eliminations: 144k's

Base Released

[QUOTE]Oops, I accidentally did three bases. :redface:[/QUOTE]

You did 3, I did 2 that's 5; / 2 or a 2.5 average.

We just slightly broke the rules:rofl:

Sierpinski Base 377
 

Primes found:

2*377^19+1
4*377^74+1
6*377^45+1

With a conjectured k of 8, this one is proven.

[quote=MyDogBuster;209388]You did 3, I did 2 that's 5; / 2 or a 2.5 average.

We just slightly broke the rules:rofl:[/quote]

Well, Mark just did 2 so now the average is 2-1/3. We need someone different to do one new base today. Then the average will be 2 and everything will be good in my world.

:missingteeth:

Sierp Base 319
 

Sierp Base 319
Conjectured k = 684
Covering Set = 5, 17, 73
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 52 mod 53(53)

Found Primes: 217k's File attached

Remaining k's: 6k's - Tested to n=25K
64*319^n+1
256*319^n+1
286*319^n+1
334*319^n+1
366*319^n+1
574*319^n+1

Trivial Factor Eliminations: 118k's

Base Released

[quote=MyDogBuster;209457]Sierp Base 319
Conjectured k = 684
Covering Set = 5, 17, 73
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 52 mod 53(53)

Found Primes: 217k's File attached

Remaining k's: 6k's - Tested to n=25K
64*319^n+1
256*319^n+1
286*319^n+1
334*319^n+1
366*319^n+1
574*319^n+1

Trivial Factor Eliminations: 118k's

Base Released[/quote]


Since the highest prime in the file is n=2817, I just thought I'd check and see if you might have missed including any higher primes.

These large bases go into these tremendous primeless gaps at times. It keeps me wondering.

[QUOTE]Since the highest prime in the file is n=2817, I just thought I'd check and see if you might have missed including any higher primes.[/QUOTE]

Just re-checked. Only 2 primes > n=2500. Another galactic void.

Reserving Sierp 373 and 379 as new to n=25K

Riesel base 302
 

Riesel base 302 is proven:
k n
2 6
3 4
4 3
5 98
6 1
7 1
8 trivial
9 5
10 1
11 74
12 1
13 conjecture

Willem.

Sierpinski Base 309
 

Primes found:

[code]
2*309^1+1
4*309^1+1
8*309^1+1
12*309^1+1
14*309^1+1
16*309^180+1
18*309^1+1
22*309^6+1
24*309^1+1
26*309^146+1
28*309^2+1
30*309^5+1
36*309^4+1
38*309^1+1
40*309^4+1
42*309^1+1
44*309^1+1
46*309^8+1
50*309^1+1
52*309^1+1
56*309^38+1
58*309^1+1
60*309^1+1
64*309^1+1
66*309^16+1
68*309^1+1
70*309^4+1
72*309^2+1
74*309^51+1
78*309^1+1
80*309^40+1
82*309^1+1
84*309^3+1
86*309^2+1
88*309^13+1
92*309^1+1
[/code]

The other k have trivial factors. With a conjectured k of 94, this conjecture is proven.

Sierp Base 373
 

Sierp Base 373
Conjectured k = 120
Covering Set = 11, 17
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 30 mod 31(31)

Found Primes: 36k's File attached

Remaining k's: Tested to n=25K
108*373^n+1
118*373^n+1

Trivial Factor Eliminations: 21k's

Base Released

Sierp Base 379
 

Sierp Base 379
Conjectured k = 246
Covering Set = 5, 19
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 6 mod 7(7)

Found Primes: 66k's - File attached

Remaining k's: Tested to n=25K
24*379^n+1
136*379^n+1
156*379^n+1

Trivial Factor Eliminations: 53k's

Base Released

Sierpinski base 272+278 is complete. Both is proven. Attached is a file with both bases. In the file is also all other k=8 sierpinski conjectures that I proved before trying to reserve them. Suite yourself, weather or not you will actually add them to the websites or not.

KEP

Ps. This also means, that even though I started and took these sierpinski conjectures bases to n=2500: 230, 335, 398, 440, 482, 587, 608, 632, 650, 797 and 818, that they are suspended and verified for deletion from my harddrive, since no further work appeared to be wanted or allowed. So for now and forward on my DualCore is focusing on PG work only :smile:

Riesel bases 293 and 335
 

Primes found:

2*293^2-1
4*293^1-1
6*293^6-1

2*335^2-1
4*335^3-1
6*335^2-1

With a conjectured k of 8, both of these are proven.

Reserving Sierp 294 & 337 as new to n=25K

[quote=KEP;209694]Sierpinski base 272+278 is complete. Both is proven. Attached is a file with both bases. In the file is also all other k=8 sierpinski conjectures that I proved before trying to reserve them. Suite yourself, weather or not you will actually add them to the websites or not.

KEP

Ps. This also means, that even though I started and took these sierpinski conjectures bases to n=2500: 230, 335, 398, 440, 482, 587, 608, 632, 650, 797 and 818, that they are suspended and verified for deletion from my harddrive, since no further work appeared to be wanted or allowed. So for now and forward on my DualCore is focusing on PG work only :smile:[/quote]

Base S230 was already shown as completed to n=25K by me with only k=4 remaining. In addition to your S272 and S278, I went ahead and also showed S293. With Mark's recent work, this leaves R272 as the only k=8 conjectured base < 300 remaining untested.

Sorry, if you want me to show the rest, you'll need to post them 2 at a time over a period of days like everyone else is doing. As tedius as it sounds, that's all that I'm asking to stem the tide somewhat.

I like your bases 58 and 60 efforts. That's what we need a lot more of. :smile:


Gary

Riesel bases 356 and 377
 

Primes found:

2*356^4-1
3*356^2-1
4*356^1-1
5*356^432-1
7*356^5-1

2*377^4-1
4*377^3-1
6*377^6-1

The other k have trivial factors. With a conjectured k of 8, these conjectures are proven.

Sierp Base 294
 

Sierp Base 294
Conjectured k = 119
Covering Set = 5, 59
Trivial Factors k == 292 mod 293(293)

Found Primes: 114k's File attached

Remaining k's: 3k's Tested to n=25K
61*294^n+1
99*294^n+1
116*294^n+1

k=1 is a GFN with no known prime

Base Released

Sierp Base 337
 

Sierp Base 337
Conjectured k = 534
Covering Set = 5, 13, 41
Trivial Factors k == 1 mod 2(2) and k = 2 mod 3(3) and k == 6 mod 7(7)

Found Primes: 151k's File attached

Remaining k's: Tested to n=25K
168*337^n+1

Trivial Factor Eliminations: 114k's

Base Released

[QUOTE=unconnected;209812]Riesel base 307, k=8
Primes:
4*307^1+1
6*307^549+1
Trivial factors k=2

Base proven.[/QUOTE]

You will need to redo this. Change the type in the script to -1 to do Riesel forms.

He deleted the incorrect work. Thanks for the catch Mark.

Unconnected, do you wish to reserve Riesel base 307?

[quote=gd_barnes;209893]Unconnected, do you wish to reserve Riesel base 307?[/quote]

Yes, I'm already working on it.

Riesel bases 440 and 482
 

Primes found:

2*440^2-1
3*440^1-1
4*440^1-1
5*440^2-1
6*440^2-1
7*440^1-1

2*482^2-1
3*482^3-1
4*482^135-1
5*482^2-1
6*482^6-1
7*482^1-1

With a conjectured k of 8, these conjectures are proven.

Note how odd base 440 is. All primes were found with n=1 and n=2.

Riesel base 307, k=8
Primes:
2*307^1-1
6*307^26262-1

Trivial factors k=4
Base proven.

[QUOTE=unconnected;209909]Riesel base 307, k=8
Primes:
2*307^1-1
6*307^26262-1

Trivial factors k=4
Base proven.[/QUOTE]

Nice! Many searchers would have stopped at n=25000.

Reserving Riesel 493 and Sierp 409 as new to n=25K

Riesel base 461, k=8
Primes:
2*461^6-1
4*461^3071-1

Trivial factors k=6
Base proven.

Riesel base 311, k=14
Primes:
2*311^2-1
4*311^5-1
8*311^2-1
10*311^1-1
12*311^146-1

Trivial factors k=6
Base proven.

Riesel base 317, k=14
Primes:
2*317^10-1
4*317^119-1
6*317^1-1
8*317^2-1
10*317^1-1
12*317^1-1

Base proven.

unconnected, Gary would like everyone to limits themselves to two results per day because too many results at one time becomes more difficult for him to manage. With the limit there are more than a couple of people who would produce a dozen or more results a day (to clean up conjectures with low k).

Thanks, Mark, for being a watchdog. :-) To clarify slightly: That's two [B]new bases[/B] per day. Also, reporting 2 completions of previous new base reservations and then reserving 2 more, all in the same day, is fine too. On existing bases, people can reserve and report as much as they want, as long as they aren't biting off too much for their resources. It's easy to manage those. The initial analysis and page/thread updates needed on new bases is what takes much longer.

Here is my general estimate: It takes me an average of ~15 mins. per new base to go through everything and generally about 5 mins. on existing bases. Of course these are only averages. Some new bases take nearly 30 mins. and others take 5-10 mins. So if 4 people do 2 new bases in a day, that's 2 hours, which includes no time for any other admin work. Even the k=8 conjectures with no algebraic factors on the Sierp side can take up to 10 mins. Here is what I do on new bases:

1. Save off or cut-paste any results/primes (most of the time).
2. Sort the primes by n descending for entry on the pages.
3. Spot verify that all k's are accounted for.
4. Open up Robert's Riesel or Sierp conjectures file and enter the base, conjecture, covering set, trivial factors, k's remaining, and top 10 primes (from #2) on the pages. (I don't take people's word for it in posts because sometimes those have typos.)
5. If a Riesel base, analyze it for 2 different kinds of algebraic factors. If a Sierp base, look for GFN primes. (Algebraic factor analysis can take ~10-15 mins. all by itself.)
6. Remove the base from one of the untested bases threads.
7. If 1k remaining, add it to the 1k thread.
8. Sometimes for new people or a tough effort, start a quick double check effort up to n=1000 or 2500.
9. Sometimes follow up with a post if new algebraic factors are found or if the prime distribution looks unusual.

That's for each and every new base that comes through. And if I have to let it go for ~5 days, I've had it take me ~8 hours, which is what happened on my last business trip. I was caught totally off guard because few new bases were coming before I left and then they came in droves starting about 2 days after I left.

I hope this clarifies a little more about why I ask for only 2 new bases at a time per day. Of course it's OK to do the occassional 3 new bases at once especially if it completes a big group of them or a bunch of them below some big round number. Of course I'll list the 3 that unconnected did (he started that original base that makes a total of 4 the day before). I'd only kindly ask that most of the time, we keep it at 2.

BTW, good job, unconnected, on finding that final prime on R307. Like Mark said, most of the time, people stop at n=25K but of course that's just because it's a nice round number that doesn't take terribly long. (I admit that I started the trend and it just kind of stuck.) Some people like KEP and Batalov like to search up to n=50K, 100K, or higher right away.


Thanks,
Gary

Riesel bases 503 and 538
 

Primes found:

2*503^860-1
4*503^1-1
6*503^22-1

2*538^8-1
3*538^1-1
5*538^1-1
6*538^14-1

The other k have trivial factors. With a conjectured k of 8, these conjectures are proven.

[QUOTE=gd_barnes;210021]Here is my general estimate: It takes me an average of ~15 mins. per new base to go through everything and generally about 5 mins. on existing bases. Of course these are only averages. Some new bases take nearly 30 mins. and others take 5-10 mins. So if 4 people do 2 new bases in a day, that's 2 hours, which includes no time for any other admin work. Even the k=8 conjectures with no algebraic factors on the Sierp side can take up to 10 mins. Here is what I do on new bases:

1. Save off or cut-paste any results/primes (most of the time).
2. Sort the primes by n descending for entry on the pages.
3. Spot verify that all k's are accounted for.
4. Open up Robert's Riesel or Sierp conjectures file and enter the base, conjecture, covering set, trivial factors, k's remaining, and top 10 primes (from #2) on the pages. (I don't take people's word for it in posts because sometimes those have typos.)
5. If a Riesel base, analyze it for 2 different kinds of algebraic factors. If a Sierp base, look for GFN primes. (Algebraic factor analysis can take ~10-15 mins. all by itself.)
6. Remove the base from one of the untested bases threads.
7. If 1k remaining, add it to the 1k thread.
8. Sometimes for new people or a tough effort, start a quick double check effort up to n=1000 or 2500.
9. Sometimes follow up with a post if new algebraic factors are found or if the prime distribution looks unusual.[/QUOTE]

This gives all of us a new appreciation for the work you do to manage this project. Thank you.

[quote=rogue;209906]Note how odd base 440 is. All primes were found with n=1 and n=2.[/quote]

That is quite strange for so many k's. I think I've had as many as 4 k's with n=1 and n=2 primes but definitely not 6 of them.

Question: I know you've already worked a bunch of the Riesel k=8 conjectures. Have you by chance worked on R272? It's a much smaller base than the others remaining untested at this point. Perhaps it has a k or two remaining and you are just posting the proven ones right now.

I ask because I thought I'd reserve it in the next couple of days if you haven't already worked on it just to knock out the final CK = 8 for b < 300 (on both sides). Regardless, feel free to take it yourself if you haven't already done so.


Gary

[QUOTE=gd_barnes;210124]Question: I know you've already worked a bunch of the Riesel k=8 conjectures. Have you by chance worked on R272? It's a much smaller base than the others remaining untested at this point. Perhaps it has a k or two remaining and you are just posting the proven ones right now.

I ask because I thought I'd reserve it in the next couple of days if you haven't already worked on it just to knock out the final CK = 8 for b < 300 (on both sides). Regardless, feel free to take it yourself if you haven't already done so.[/QUOTE]

R272 had remaining k (tested to n=2000), so I have left it alone for now. I did not investigate algebraic factorizations so it is possible that one of those would be needed to prove the conjecture. I was going to take another base before Friday, but hadn't decided on anything specific. It was most likely going to be a conjecture with a single k remaining. R272 would be a good choice, but I'll let you take it. I'll find something else as there is so much to choose from. It's like going to the ice cream shop and seeing more than 100 flavors and having difficulty choosing the one that will taste the best...

[quote=rogue;210126]R272 had remaining k (tested to n=2000), so I have left it alone for now. I did not investigate algebraic factorizations so it is possible that one of those would be needed to prove the conjecture. I was going to take another base before Friday, but hadn't decided on anything specific. It was most likely going to be a conjecture with a single k remaining. R272 would be a good choice, but I'll let you take it. I'll find something else as there is so much to choose from. It's like going to the ice cream shop and seeing more than 100 flavors and having difficulty choosing the one that will taste the best...[/quote]

OK, I'll reserve R272 to n=25K.

Doing some quick math in my head :smile: on the algebraic factors:

272 = 2^4*17
-and-
273 = 3*7*13

To determine which numeric factor could combine with algebraic factors to make a full covering set, one must go to the factorization of b+1; in this case 273. Since 3 and 7 are not possible factors as per the algebraic factors thread and 13 is, that's the only one applicable. Since k must be m^2 and m must be m==(5 or 8 mod 13) when the numeric factor is 13, the lowest possible k that could be eliminated would be k=5^2=25. So with a conjecture of k=8, nothing can be removed here. That's the "old" or "classical" kind of algebraic factors.

For the new kind, you have to remove the squared part of b to get a multiplier. (If there is no squared part, then the new kind are not applicable.) In this case 272 / 2^4 = 17. So we have k must be 17*m^2 and m must be m==(3 or 10 mod 13). This means that the lowest k would be k=17*3^2=153. Once again too high for a conjecture of k=8. That's the "new" kind of algebraic factors found by Serge. (Interestingly we had already found it on bases 24 and 54 long before Serge started participating but we just didn't realize it. I just thought it was specific to only those bases. Serge's analysis showed that it was potentially applicable to all bases.)

Therefore nothing can be eliminated by algebraic factors on R272.

BTW, the modulos for the m-values were determined by nothing more than trial and error on my part over a series of bases with the specific numeric factorizations (in this case 13). I do know that x and y add up to f in all cases and I do know that there are no more and no less than 2 modulos (all shown in the algebraic factors thread for the various factors). That is the 5 and 8 in the m==(5 or 8 mod 13) add up to the 13. I do not have a proof for this but I'd be willing to bet that someone could prove it.

That's the mental process that I go through to show them on the pages. I then do a quick check using Alperton's applet. Sometimes I find that I missed something or miscalculated it.

I mention all this detail in case it helps someone else determine the algebraic factors ahead of time.


Gary

R236 is complete to n=25K; k=67 & 78 remaining; base released.

R248 is complete to n=25K; only k=56 remaining; base released.

Another big prime hole: R236 highest prime is currently 59*236^1786-1.

Riesel base 263, k=10
Primes:
2*263^2-1
4*263^1-1
6*263^2-1
8*263^2-1

Base proven.

R272 with CK=8 is complete to n=25K; only k=6 remains; base released.

Riesel Base 493
 

Riesel Base 493
Conjectured k = 170
Covering Set = 13, 19
Trivial Factors k == 1 mod 2(2) and k == 1 mod 3(3) and k == 1 and 41(41)

Found Primes: 54k's - File attached

Remaining k's: 1k - Tested to n=25K
92*493^n-1

Trivial Factor Eliminations: 29k's

Base Released

Sierp Base 409
 

Sierp Base 409
Conjectured k = 124
Covering Set = 5, 41
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 16 mod 17(17)

Found Primes: 36k's - File attached

Remaining k's: 1k - Tested to n=25K
6*409^n+1

Trivial Factor Eliminations: 24k's

Base Released

S356 and S437 k=8 conjectures proven and added to the pages.

Riesel bases 296 and 395
 

Primes found:
2*296^36-1
3*296^1-1
4*296^27-1
5*296^8-1
7*296^3-1
8*296^16-1
9*296^1-1

2*395^396-1
4*395^1-1
6*395^14-1
8*395^2-1

The other k have trivial factors. With a conjectured k of 10, these conjectures are proven.

S473 k=8 conjecture proven and added to the pages.

Riesel base 428
 

Primes found:

2*428^4-1
3*428^1-1
4*428^55-1
5*428^2-1
6*428^2-1
7*428^3-1
9*428^1-1

The other k have trivial factors. With a conjectured k of 10, this conjecture is proven.

Riesel Base 398
 

Reserving this base to at least n=25000.

Serge reported in a Mar. 29th Email that S405 k=106 is complete to n=50K. The base is now released.

Riesel base 398
 

Primes found:

2*398^32-1
3*398^1-1
4*398^3-1
5*398^22-1
6*398^2-1

k=7 remains. This has been tested to n=25000. I am releasing the base.

Reserving Riesel 363 and 376 as new to n=25K

Riesel base 467, k=14

Primes:
2*467^36-1
4*467^1-1
6*467^1-1
8*467^20-1
10*467^15-1
12*467^2-1

Base proven.

Reserving S383 as new. To at least n=25K :smile:

Status update for S58 and S60 will come this friday or saturday, with at least 4 new primes to show for S60.

Regards

KEP

2*461^n+1 n=25K-75.7K is done. No primes. Residues emailed.
(I ran it to test the time, then forgot about it. Now stopped at n=75735.)