Mathew has reported that R601 is complete to n=50K. There is nothing to report and the base is released.

S882
 

Sierp Base 882
Conjectured k = 5297
Covering Set = 5, 37, 883
Trivial Factors k == 880 mod 881(881)

Found Primes: 5209k's - File emailed

Remaining: 76k's - Tested to n=25K - File emailed

Trivial Factor Eliminations: 6k's

MOB Eliminations: 3k's - File emailed

GFN Eliminations: 1k - File emailed
882

Base Released

S988
 

Sierp Base 988
Conjectured k = 1678
Covering Set = 23, 43
Trivial Factors k == 2 mod 3(3) and k == 6 mod 7 (7) and k == 46 mod 47 (47)

Found Primes: 923k's - File emailed

Remaining: 13k's - Tested to n=25K - File emailed

Trivial Factor Eliminations: 739k's

GFN: 1k - File emailed
988

Base Released

R697 R952
 

Reserving R697 & R952 s new to n=25K

S723
 

Sierp Base 723
Conjectured k = 2354
Covering Set = 5, 13, 181
Trivial Factors k == 1 mod 2(2) and 18 mod 19(19)

Found Primes: 1087k's - File emailed

Remaining: 27k's - Tested to n=25K - File emailed

Trivial Factor Eliminations: 62k's

Base Released

Reserving S625 as new to n=25K.

It has about a hundred k's left to test after first weeding. That is after taking off the list some already known S5 primes and 8 S25 well tested k's. It also has four excluded Aurifeuillian k's (because 625 itself is the 4th power)!

[QUOTE=Batalov;263573]Reserving S625 as new to n=25K.

It has about a hundred k's left to test after first weeding. That is after taking off the list some already known S5 primes and 8 S25 well tested k's. It also has four excluded Aurifeuillian k's (because 625 itself is the 4th power)![/QUOTE]

I show that there are 6 Aurifeuillian k's. To verify that I'm understanding the term "Aurifeuillian" correctly, I take that to mean k's that are of the form 4*q^4, which means that the form 4*q^4+1 factors as (2*m^2+2m+1)*(2*m^2-2m+1). Regardless, I show the k's that are eliminated by such "full algebraic factors" as 4, 1024, 2500, 5184, 9604, & 16384. k=64 & 324 have a trivial factor of 13 so don't require the algebraic factors to eliminate them.

Let me know if you agree with this.

yep, six, if we pull 2500 out in the MOB bin. (And 64 and 324 are in the trivial bin). All of them are excluded, anyway.

The MOB bin has to be sorted after all is done. There's still 3750 in it, and it will go where 6 will go. Right now, 6 is still undecided.

Around now, down to 80 k's and 8 k's common with S25:
222 (100K for base 25; for base 625, half that)
6436 (275.3K)
7528 (289.1K)
10218 (100K)
10918 (280.1K)
12864 (100K)
13548 (100K)
15588 (100K)

Right now the top 5 are:
12988*625^31700+1
14110*625^31029+1
6082*625^22718+1
1146*625^13948+1
2190*625^9139+1
(and it is obvious that the largest ones are borrowed from S5;
using "^[[:digit:]]{1,}*5^[[:digit:]]{1,}+1" and "Type: all" in [URL="http://primes.utm.edu/primes/search.php"]adv.search[/URL])

S877
 

Sierp Base 877
Conjectured k = 2182
Covering Set = 5, 7, 13, 37, 139
Trivial Factors k == 1 mod 2(2) and k == 2 mod 3(3) and k == 72 mod 73(73)

Found Primes: 698k's - File emailed

Remaining: 18k's - Tested to n=25K - File emailed

Trivial Factor Eliminations: 374k's

Base Released

Taking R1001 and S1002.

S758
 

S758 tested n=100K-200K - Nothing found

Results emailed - Base released