[QUOTE=Puzzle-Peter;270419]Let's try for a new highest CK with 3 ks remaining. Reserving R31 to n=500k. I'll sieve to n=1M though.[/QUOTE]

First goal achieved: [FONT=&quot]43902*31^251859-1 is prime
[/FONT]

Serge has reported that S27 is at n=~550K. He is continuing to n=~600K.

[QUOTE]Serge has reported that S27 is at n=~550K. He is continuing to n=~600K. [/QUOTE]

And my R27 is at 835K and continuing to 1M

s17 is at n~1.22M

s19 n~72k, here are the primes for n=50k till 70k:
[CODE]532306*19^50380+1
191896*19^50428+1
517284*19^50467+1
622366*19^50508+1
293404*19^50611+1
352504*19^51331+1
304356*19^51528+1
464266*19^51780+1
129174*19^51819+1
213516*19^51938+1
387654*19^52045+1
557910*19^52367+1
565284*19^52699+1
565944*19^52919+1
573204*19^53029+1
363864*19^53127+1
697654*19^53293+1
395776*19^53594+1
174586*19^53720+1
87016*19^53864+1
142546*19^54120+1
226134*19^54399+1
346084*19^54489+1
532624*19^54553+1
494016*19^54666+1
221506*19^54826+1
474726*19^55006+1
351694*19^55393+1
499444*19^55415+1
147846*19^55850+1
106954*19^55913+1
379146*19^55920+1
220294*19^56355+1
165666*19^56848+1
277924*19^56999+1
424404*19^57013+1
509134*19^57053+1
631566*19^57082+1
242446*19^57426+1
395854*19^57473+1
277806*19^57526+1
327754*19^57567+1
738144*19^57593+1
417264*19^57679+1
12114*19^58035+1
590094*19^58325+1
763204*19^58415+1
625966*19^58684+1
538606*19^58720+1
343494*19^59129+1
377604*19^59199+1
277084*19^59513+1
15348*19^59565+1
125794*19^59595+1
366736*19^59698+1
245284*19^59739+1
182796*19^59952+1
707376*19^59992+1
736986*19^60040+1
401116*19^60794+1
740394*19^61191+1
379116*19^61218+1
506256*19^61226+1
457246*19^61394+1
138484*19^61783+1
337374*19^61945+1
188296*19^62268+1
349956*19^62316+1
66226*19^62458+1
143076*19^62472+1
14284*19^62547+1
100816*19^62614+1
201526*19^62654+1
762504*19^63185+1
733254*19^63809+1
327414*19^64129+1
702934*19^64403+1
634134*19^64497+1
557926*19^64680+1
546994*19^64789+1
56154*19^64865+1
40344*19^65201+1
678996*19^65382+1
638044*19^65435+1
467716*19^65870+1
401476*19^66000+1
68536*19^66110+1
294486*19^66830+1
708234*19^67281+1
621954*19^67463+1
493474*19^68323+1
377694*19^68587+1
257826*19^68852+1
678264*19^69173+1
46006*19^69920+1[/CODE]
Continuing both.

[QUOTE=Xentar;278572]s17 is at n~1.22M

s19 n~72k, here are the primes for n=50k till 70k:Continuing both.[/QUOTE]

Nice work Xentar!

For S19, 75 primes for n=54K-70K leaves 773 k's remaining at n=70K.

R27
 

R27 tested to n=850K - nothing found - continuing to 1M

Status report
 

Base=10 (Sierpinski + Riesel) tested till n=710000

R19 is complete to n=50K

267 primes found

Base released

R31 tested n=250k to 300k, no luck. Continuing...

R27
 

R27 tested to n=860K - nothing found - continuing to 1M

status report
 

Base=10 (Sierpinski + Riesel) tested till n=720000