Sierp 677
 

Sierp Base 677
Conjectured k = 112
Covering Set = 3, 113
Trivial Factors k == 1 mod 2(2) and k == 12 mod 13(13)

Found Primes: 50k's - File emailed

Remaining: 3k's - Tested to n=25K
34*677^n+1

Trivial Factor Eliminations: 4k's

Base Released

HTML created

Reserving several bases with CK<100 to n=25K from my former k=2 search, all that have only 1 or 2 k's remaining at n=10K, as follows:

R581
R845
R968
S626
S695
S752
S758
S917

Many are extremely low weight and only one has a CK>50. All should complete to n=25K in ~2-3 days running on 2 cores. Hopefully I'll prove 1 or 2 of them.

This should add a few bases to the 1k thread. :-)

Ian, I'll take care of showing these on the pages so that we aren't sending files back and forth.


Gary

Reserving the remaining five CK=10 and 12 Sierp bases (1 is b<500 shown in b=251-500 thread) to n=25K:

S563
S593
S714
S828

This is the last of my testing small conjectured bases for an extended period. The small Sierp bases are beginning to catch up with the Riesel bases now.

The lowest CK on either side is now 14.

ETA is < 2 days on 1 core.

Reserving Riesel 543 as new to n=25K

[quote=gd_barnes;215483]Reserving several bases with CK<100 to n=25K from my former k=2 search, all that have only 1 or 2 k's remaining at n=10K, as follows:

R581
R845
R968
S626
S695
S752
S758
S917

Gary[/quote]


All 8 bases from this former k=2 search that had 1 or 2 k's remaining are complete to n=25K. All are released.

Not a single base was proven! Primes for n=5K-25K:

2*758^8309+1
58*581^16145-1

Both were 2k bases so 1k still remains. :-( Final status:

[code]
k(s)
base CK remain highest prime
R581 98 2 58*581^16145-1
R845 46 2 22*845^593-1
R968 16 4 2*968^1750-1
S626 10 2 5*626^2069+1
S695 28 2,8 26*695^1771+1
S752 16 2 15*752^1128+1
S758 10 8 2*758^8309+1
S917 16 2 8*917^53+1
[/code]

7 more bases for the 1k thread! More to follow with the CK=10 & CK=12 finishing effort...

R702 is complete to n=25
CK=75
k=36 is removed by algebraic factorizations

1k remains k=32

Sorry Gary another base to the 1k thread

Attached are the results.

[quote=gd_barnes;215595]Reserving the remaining five CK=10 and 12 Sierp bases (1 is b<500 shown in b=251-500 thread) to n=25K:

S563
S593
S714
S828
[/quote]

All of the remaining Sierp CK=10 and 12 bases are complete to n=25K. All are released. 2 were proven, 2 had 1k remaining (1 of them in the b<=500 thread), and 1 had 2k remaining.

Final status:
[code]
k(s)
base CK remain highest prime
S563 12 proven 4*563^3958+1
S593 10 2,8 6*593^1+1 (pitiful!)
S714 12 proven 10*714^7839+1
S828 12 8 5*828^6+1
[/code]

2 more bases for a total of 9 for the 1k thread over the last 2 days!

Reserving S999 to n=25K.

Riesel Base 798
Conjectured k = 339
Covering Set = 5, 13, 17
Trivial Factors k == 1 mod 797(797)

Found Primes: 328k's - File emailed

Remaining: 7k's - File emailed - Tested to n=25K
188*798^n-1
279*798^n-1
283*798^n-1
302*798^n-1
307*798^n-1
317*798^n-1
322*798^n-1

k=16, 169 proven composite by partial algebraic factors

Base Released

Sierp Base 596
Conjectured k = 200
Covering Set = 3, 199
Trivial Factors k == 4 mod 5(5)
k == 6 mod 7(7)
k == 16 mod 17(17)

Found Primes: 122k's - File emailed

Remaining: 5k's - Tested to n=25K
8*596^n+1
71*596^n+1
121*596^n+1
136*596^n+1
151*596^n+1

Trivial Factor Eliminations: 71k's

Base Released

Reserving the folllowing "1ker's" to n=50K.

30*514^n-1
22*900^n-1
8*908^n-1
74*947^n-1
4*968^n-1