I added a P.S. above, and ah yes,
[FONT=Arial Narrow]230*780^11159+1 is prime! (25.1733s+0.0018s)[/FONT]
making S780 now a single-k contender (passed 28K recently for k=43).

[quote=henryzz;207729]
105*784^14268+1
139*784^23965+1
[/quote]
I should have mentioned:
riesel 784 now only has one k remaining

[quote=henryzz;207800]I should have mentioned:
riesel 784 now only has one k remaining[/quote]

I already noticed that Sierp 784 had one k remaining and added it to the official list.

Serge has Riesel 784 reserved with 2 k's remaining. :smile:

Riesel 506
 

Riesel Base 506
Conjectured k = 14
Covering Set = 3, 13
Trivial Factors k == 1 mod 5(5) and k == 1 mod 101(101)

Found Primes:
2*506^16-1
3*506^2-1
4*506^11-1
5*506^2-1
7*506^1-1
8*506^146-1
9*506^3-1
10*506^1-1
12*506^2-1
13*506^1-1

Trivial Factor Eliminations:
6
11

Conjecture Proven

Sierp Base 506
 

Sierp Base 506
Conjectured k = 25
Covering Set = 3, 13
Trivial Factors k == 4 mod 5(5) and k == 100 mod 101(101)

Found Primes:
2*506^1+1
3*506^3+1
5*506^1+1
6*506^1+1
7*506^6+1
8*506^1+1
10*506^2+1
11*506^269+1
12*506^1+1
13*506^2+1
15*506^1+1
16*506^1066+1
17*506^3+1
18*506^1+1
20*506^11+1
21*506^1+1
22*506^22+1
23*506^3+1

Trivial Factor Eliminations:
4
9
14
19
24

Conjecture Proven

[QUOTE=gd_barnes;207794]Mark,

Did you want to post the primes and k's remaining on R928? If so, I'll show them on the pages.
[/QUOTE]

Go ahead and show them. I doubt anyone will poach the base.

[QUOTE=Batalov;207793]Yes. I've sieved to 900K but will have a look how slow it will be at 600K.

base-3 is testing faster (PFGW doesn't decompose the base and goes into awkward FFT sizes).
example:

[FONT=Arial Narrow]-f0 -l../Bextra -q8*3^200017-1[/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]20K[/B] on 8*3^200017-1[/FONT]
[FONT=Arial Narrow]8*3^200017-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]96.7036s[/B]+0.0059s)[/FONT]
[FONT=Arial Narrow]Done.[/FONT]

[FONT=Arial Narrow]-f0 -l../Bextra -q24*729^33336-1[/FONT]
[FONT=Arial Narrow]PFGW Version 3.3.1.20100111.Win_Dev [GWNUM 25.13][/FONT]
[FONT=Arial Narrow]Output logging to file ../Bextra[/FONT]
[FONT=Arial Narrow]No factoring at all, not even trivial division[/FONT]
[FONT=Arial Narrow]Special modular reduction using FFT length [B]40K[/B] on 24*729^33336-1[/FONT]
[FONT=Arial Narrow]24*729^33336-1 is composite: RES64: [2A3BFDAF3B7C8E79] ([B]196.6488s[/B]+0.0059s)[/FONT]

[FONT=Verdana]For the same reduction reason, I'd like to reserve R784 to 50K (in base-28, 100K). Will try to get it to a single-k status.[/FONT]


[COLOR=green]P.S. I've been doing the same with S961 as far as I remember, when I first found this. [/COLOR]
[COLOR=green]I thought that the new version was immune to that, but found the same after testing.[/COLOR][/QUOTE]

The FFT size is chosen by gwnum. PFGW has little control over it. I could modify PFGW to look for bases that are perfect powers and change the parameters that it passes to gwnum.

[quote=rogue;207820]The FFT size is chosen by gwnum. PFGW has little control over it. I could modify PFGW to look for bases that are perfect powers and change the parameters that it passes to gwnum.[/quote]
PFGW could have passed the faster 8*3^200017-1 to gwnum rather than 24*729^33336-1 when asked to test 24*729^33336-1

[quote=rogue;207818]Go ahead and show them. I doubt anyone will poach the base.[/quote]

???

How can I show them? You didn't post them. lol

What I'm asking is that you post (i.e. attach) them.

[QUOTE=gd_barnes;207846]???

How can I show them? You didn't post them. lol

What I'm asking is that you post (i.e. attach) them.[/QUOTE]

Oops. I swear I had attached it, but I suspect I chose the file without uploading. It is attached to this post.

[quote=rogue;207820]The FFT size is chosen by gwnum. PFGW has little control over it. I could modify PFGW to look for bases that are perfect powers and change the parameters that it passes to gwnum.[/quote]
Intuitively, nobody expects that effect, so I didn't mean it as any criticism.

That would be a very nice addition. Time savings! Plus, if you will be implementing this, then you may want to chisel the new smaller base from the [I]k[/I] and add it to the exponent.

If you (internally to PF, before GWnum) completely factor the [I]k[/I] and [I]b[/I], pfgw could also immediately catch and report some algebraic factorizations; here's a test case: suppose I submit [FONT=Fixedsys]26*234^149885-1[/FONT][FONT=Verdana] (or amidst the ABC file) then[/FONT]

[FONT=Courier New]k= 26=2*13[/FONT]
[FONT=Courier New]b=234=2*3^2*13[/FONT]
[FONT=Courier New]n is odd[/FONT]

...and the program could immediately report "is composite by algebraic" and optionally report the factors (or the smaller one): all a^2-b^2 and a^odd+-b^odd could be caught (it is not always trivial to catch all of them by eye, right?).

I am sure a lot of users could be very happy with that addition.

-Serge


[SIZE=1][COLOR=green]P.S. I thought of a small obvious caveat in this algebra (not relevant for the Sierp/Riesel forms): [/COLOR][/SIZE]
[SIZE=1][COLOR=green]If a-b=1 (which is rare but we don't want any induced bugs), then no use for the minus form. (Example 6^2-5^2.)[/COLOR][/SIZE]