Sierp 15 tested n=10K-25K with the following primes found:

6598*15^11715+1
977594*15^12860+1
148548*15^13101+1
966148*15^14630+1
62900*15^16936+1
633342*15^22404+1

Range Released

R26 is at n=350K; nothing to report; continuing to n=400K.

I have completed sieving R22 & S22 for n=300K-1M to P=50T. Starting from P=7T, this was a relatively substantial effort requiring > 2 CPU months. It should be sufficient for testing both sides up to n=500K. Updated sieve files are now posted on the pages.

These are some very nice files for searching! The one k remaining for R22 that is on the recommended list at n=400K is now ready and waiting to go. :smile: S22 is reserved by the PRPnet mini drive to n=300K but is available for n>300K. Our current plan is to switch over the mini drive to a different base at n=300K.

That's the good news. Now the bad news:

If we find no primes up to n=500K on either side, the optimal sieve depth for n=500K-1M when combining them is P>250T! :no: (As VBCurtis pointed out at NPLB and I subsequently confirmed with my own calculations, CPU time is actually lost if we try to break off ranges and sieve the remaining range higher if the ratio of high n to low n is <= 2. That is, unless we make the determination that the effort will not be complete before CPU/software capacity/speeds have increased substantially; something that I am a proponent of taking into consideration.) Therefore although it will probably take a little more overall CPU time, we may want to consider separating the sieves for the 2 sides since the optimal for the one k will be at least somewhat lower but more importantly will sieve far faster, which would give us a better chance of proving it in a more reasonable timeframe. 4 k's vs. 1 k is a borderline case on whether they should be sieved together.

The best thing that could happen is that we find a prime for k=4233 on the Sierp side. It is by far the highest weight of the 5 combined k's remaining. Doing so would reduce the overall optimum sieve depth quite a bit.


Gary

Reserving R22 for n=400K-500K. I'll start on it after finishing R26 to n=400K in < 1 week.

Reserving 404*23^n-1.

R26 is complete to n=400K; nothing to report; base released.

Status report
 

Base=10 (Sierpinski + Riesel) tested till n=490000.

S30 status at n=270K, no primes.

Continuing to n=300K.

Attached is the updated sieve file for n=300K-500K, sieved to P=15T.

R22 is at n=450K; nothing to report; continuing to n=500K.

S7: k=242334
 

A quick LLR V3.8.1 test and found this:

242334*7^33795+1 is prime! Time : 19.642 sec.
242334*7^34451+1 is prime! Time : 19.627 sec.

n=30k-35k done

Verified with pfgw:

Primality testing 242334*7^33795+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
242334*7^33795+1 is prime! (19.1742s+0.0020s)
Primality testing 242334*7^34451+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
242334*7^34451+1 is prime! (43.4830s+0.0020s)

[quote=kar_bon;221705]A quick LLR V3.8.1 test and found this:

242334*7^33795+1 is prime! Time : 19.642 sec.
242334*7^34451+1 is prime! Time : 19.627 sec.

n=30k-35k done

Verified with pfgw:

Primality testing 242334*7^33795+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
242334*7^33795+1 is prime! (19.1742s+0.0020s)
Primality testing 242334*7^34451+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
242334*7^34451+1 is prime! (43.4830s+0.0020s)[/quote]
Note that LLR 3.8.1 does an N-1 test on such numbers, and therefore a second proof with PFGW is unneeded. As a general rule, whenever LLR says "x is prime!" it is a proven prime, whereas it only says "is a probable prime" otherwise.