Reserving Riesel 870 and 922 as new to n=25K

Riesel base 593
 

Primes found:

2*593^4-1
4*593^1-1
6*593^1-1
8*593^2-1

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

Riesel Base 566
 

This base has been tested to n=25000.

Primes found:
2*566^4-1
3*566^1-1
4*566^23873-1
5*566^2-1

k=1 and k=6 have trivial factors. k=7 remains. This base is released. I was pleasantly surprised that k=4 has a prime because I was wondering if I missed an algebraic factorization.

Yes Gary, I know that I have submitted three results today and have one reservation. Fortunately none of these bases have any algebraic factorizations for you to worry about. I won't be posting any results tomorrow.

reserving riesel 752
there are 13 ks remaining at n=2500 which i think is high for a conjecture of ~100

Riesel base 800, k=88
Primes n>10000:
53*800^14346-1
23*800^20452-1
5*800^20508-1

Remaining k's:
4*800^n-1
8*800^n-1
25*800^n-1

Are there any algebraic factorizations?

Some for each of them, but no 'deadly' eliminations, just flesh wounds.

n=0|2: square for 4*800^n-1

0|3 2^3 8*800^n-1
1|2 80^2 8*800^n-1

0|2 5^2 25*800^n-1
4|5 50^5 25*800^n-1

So, 4*800^n-1: odd n are alive and still need work,
8*800^n-1: n=2,4(mod 6) survive and need work,
25*800^n-1: n=1,3,5,7(mod 10) survive and need work.

Riesel base 928 update
 

Primes found:

[code]
489*928^11587-1
662*928^12427-1
885*928^10067-1
1367*928^10874-1
1521*928^11273-1
1728*928^12796-1
1851*928^11633-1
2286*928^14583-1
2522*928^10962-1
3908*928^11388-1
4005*928^13723-1
4293*928^14817-1
4458*928^12192-1
4983*928^10496-1
5342*928^10223-1
5364*928^10032-1
5979*928^10727-1
6038*928^13038-1
6122*928^11268-1
6143*928^11661-1
6516*928^11211-1
6563*928^12498-1
6818*928^10874-1
6972*928^11015-1
7914*928^11256-1
8006*928^13073-1
8171*928^10299-1
8750*928^12347-1
8858*928^11898-1
8948*928^13820-1
9647*928^14815-1
10887*928^12588-1
11903*928^10068-1
12026*928^10735-1
12149*928^11956-1
12189*928^10587-1
12561*928^11847-1
12942*928^12763-1
12978*928^13256-1
13080*928^14344-1
13116*928^10195-1
13154*928^11209-1
13274*928^12335-1
13517*928^11186-1
13572*928^12364-1
13997*928^11407-1
14001*928^12866-1
14897*928^12352-1
15149*928^11228-1
15248*928^12801-1
15353*928^10844-1
15689*928^10304-1
16107*928^10095-1
16397*928^13428-1
16692*928^10771-1
17193*928^14120-1
17420*928^12570-1
17616*928^13117-1
17802*928^10796-1
17991*928^12199-1
19175*928^10668-1
19202*928^12151-1
19853*928^13856-1
20253*928^11465-1
20282*928^13175-1
20793*928^12220-1
20936*928^11913-1
22227*928^10140-1
22790*928^11385-1
23081*928^14553-1
23193*928^12081-1
23501*928^11139-1
23552*928^10218-1
23697*928^13875-1
24060*928^10010-1
24645*928^10535-1
25841*928^12921-1
26055*928^11830-1
26991*928^10222-1
27341*928^13494-1
27567*928^10916-1
27666*928^10446-1
27908*928^14436-1
28257*928^14390-1
29153*928^11120-1
29421*928^11517-1
30471*928^14643-1
30501*928^12338-1
30831*928^13810-1
31292*928^11183-1
31439*928^10352-1
31458*928^11013-1
31739*928^12856-1
32022*928^14983-1
32288*928^12034-1
[/code]

Tested to n=15000 and continuing.

[quote=unconnected;210521]Riesel base 800, k=88
Primes n>10000:
53*800^14346-1
23*800^20452-1
5*800^20508-1

Remaining k's:
4*800^n-1
8*800^n-1
25*800^n-1

Are there any algebraic factorizations?[/quote]

Unconnected,

Is your search limit n=25K on this? I assume you are releasing the base. Is that correct?


Gary

Serge just reported in an Email that he is working on S736 and has only 1 k remaining, possibly searched to n=50K.

Serge, I'll just show the base as reserved by you for now and will await more details before showing anything else.


Gary

Here's the bottom of the file:
[FONT=Arial Narrow]Special modular reduction using all-complex FFT length 48K on 12*736^49762+1
12*736^49762+1 is composite: RES64: [AC939B6DF751B4C0] (486.2651s+0.0077s)
Special modular reduction using all-complex FFT length 48K on 12*736^49838+1
12*736^49838+1 is composite: RES64: [9B89781FA2896439] (486.2233s+0.0078s)
Special modular reduction using all-complex FFT length 48K on 12*736^49878+1
12*736^49878+1 is composite: RES64: [413237B012FC9095] (487.6378s+0.0077s)
Special modular reduction using all-complex FFT length 48K on 12*736^49930+1
12*736^49930+1 is composite: RES64: [4932E6E3709B79DD] (488.2011s+0.0080s)
Special modular reduction using all-complex FFT length 48K on 12*736^49942+1
12*736^49942+1 is composite: RES64: [D67226A6C349F805] (487.2219s+0.0077s)[/FONT]

I'll send you the complete set by email. Only [I]k[/I]=12 remains at 50K and the base is released (I have too many reserved; I will try to round them up.)

OK, I got it. For public reference, here are the statuses reported in the Email:

S736 is complete to n=50K; only k=12 remaining; base released.

R931 is complete to n=30K; 4 k's remaining; base released.

With a CK of 3960, R931 is yet another remarkably heavy-weight b==(1 mod 30) base.