It depends on the version of msieve; the most recent ones use a full-strength primality test on the factors and report them as 'p'.

The older versions use 20 passes of Miller-Rabin with random bases. Not much thought had gone into the primality tests Msieve uses until David Cleaver added his APRCL code. Even with the old version, inputs less than the square of the trial factoring bound (10^5) are declared prime. There had been requests for primality proving for years, but I couldn't justify the effort required. It was hard to argue with someone doing all the work, though :)

I'll take 6883_61_minus1 next.

We wonder how far "iceweasel" will "grow" over time?

There is only one way to find out!

[CODE]top - 15:25:14 up 16 days, 17:59, 6 users, load average: 1.68, 1.41, 1.29
Tasks: 171 total, 2 running, 169 sleeping, 0 stopped, 0 zombie
%Cpu0 : 1.4 us, 0.2 sy, 79.8 ni, 18.5 id, 0.0 wa, 0.0 hi, 0.0 si, 0.0 st
%Cpu1 : 1.2 us, 0.3 sy, 79.4 ni, 19.0 id, 0.0 wa, 0.0 hi, 0.0 si, 0.0 st
%Cpu2 : 5.6 us, 1.1 sy, 7.2 ni, 85.8 id, 0.2 wa, 0.0 hi, 0.0 si, 0.0 st
%Cpu3 : 5.1 us, 1.0 sy, 11.5 ni, 82.2 id, 0.1 wa, 0.0 hi, 0.0 si, 0.0 st
MiB Mem: 16010.64+total, 12386.28+used, 3624.359 free, 54.762 buffers
MiB Swap: 0.000 total, 0.000 used, 0.000 free. 7141.863 cached Mem

PID USER PR NI VIRT RES SHR S %CPU %MEM TIME+ nTH P COMMAND
15228 m 39 19 2755.7m 2.679g 1.9m R 100.0 17.1 5308:46 1 2 ./msieve -v -nc target_density=112 -t 1
5235 m 20 0 6698.2m 1.690g 53.2m S 6.4 10.8 2344:49 480 1 iceweasel[/CODE]:max:

I'll take 4091^71-1

ETA evening of 3 February

C211_121_75
 

[CODE]p68 factor: 22005275904080406107054935816620608456610359842370122577578909913467
p144 factor: 179228860624350281984700611345290739523366763846812168770969826799804801442859659626123581024327695739728437738059506035178171116927770754000849[/CODE]

8_269_minus_7_269 complete
 

[QUOTE=jyb;423893]I can take 8_269_minus_7_269 for post-processing.[/QUOTE]

Whoa, this one did not get enough ECM, apparently. Although given the 3-way split, even if the 47-digit factor were known, it would still have required the same NFS effort.

[code]
p47 factor: 63114004184218450772318216431038158607109067561
p67 factor: 4741515390811528985749791051638497031569341941056417119817991873989
p120 factor: 747244692061433908388323714497667107975207477527795863826868403853526380407802412454124839197349709661613622645915326801
[/code]

What SNFS difficulty was it? SNFS-230 would merit something near t48, which would have a 20-25% chance to miss a factor that size.

6883_61_minus1 factored
 

32.5 hours to solve a 7.45M matrix on mostly idle Core-i5/2500K with -t 4, target_density=116 (TD=120 failed).
[CODE]p68 factor: 84273559293405121928979399486848406700565800617077898448855241626079
p115 factor: 5245956891208220007358651770865998231614272255190924227608335479651400690815208991333212112292678008643404661706329[/CODE]

C259_131_97 done
 

[code]
Thu Jan 28 02:53:50 2016 prp63 factor: 283614117787866468094423360694273484828422170197058254732041677
Thu Jan 28 02:53:50 2016 prp83 factor: 18465028266988351471348374598083345672675509533258185596008206139569807614139701509
Thu Jan 28 02:53:50 2016 prp114 factor: 981108110414542945638245088752661429623158530523661605003815000859986790006193284288333961708447242654941015393793
[/code]

363.9 hours on six threads i7/5820K for a 25.8M matrix with density 110.

Log attached

[QUOTE=VBCurtis;424359]What SNFS difficulty was it? SNFS-230 would merit something near t48, which would have a 20-25% chance to miss a factor that size.[/QUOTE]

How did you calculate t48 for an SNFS 230? I thought the rule of thumb was about 2/9 for SNFS jobs, making it more like a t51.

But in any case, this job was actually an SNFS 245, as you can see from the NFS@Home status page.