Perhaps some of you may have noticed the recent progress in the

Very Prime Riesel and Sierpinski k thread started by Robert Smith.

About one month ago Robert found a Riesel k, a so called VPS (Very Prime Series), for which we discovered

**201 primes** so far (up to n=480k).

This is quite extraordinary, since there are no other known series with 200 primes so far (actually no other series has 183 or more known primes).

Since our resources are limited we are offering this k to the RPS community.

The candidate is

**k=22544089918041953*3*5*11*13*19*29*37*53*59*61*67*83*101*107*131** (=1480472640274704456611717878515654164205), a 40 digits number. Its

**Nash weight is 8818** (= "very high").

Now the unpleasant facts about this k:

~~LLR cannot handle such large values of k, therefore one has to use PFGW.~~
A single LLR test or a PRP test using PFGW typically takes 4-5 times as long as a LLR test for an "ordinary" k of 3-5 digits having the same n.

The attached file contains the range n=500-800k sieved up to p=6.34T, which should keep us busy for a while. Please help yourself to pick a suitable range for your machine(s).

Well, there would be no Top5000 credit for primes found in this range.

But with your help we could drive this k into the megabit range quite soon!

**Status**
Code:

Range Tested by Status
1-250,000 - Robert - Complete (191 primes)
250,001-500,000 - Thomas - Complete (14 primes)
500,001-600,000 - Lennart - Complete (4 primes)
600,001-610,000 - Antonio - Complete (2 primes)
610,001-612,000 - lsoule - Complete
612,001-614,000 - Robert - Complete
614,001-620,000 - lsoule - Complete
620,001-630,000 - Batalov - Complete
630,001-635,000 - Antonio - Complete
635,001-640,000 - lsoule - Complete (1 prime)
640,001-730,000 - Batalov - Complete (1 prime)
730,001-732,000 - Kosmaj - Complete
732,001-740,000 - lsoule - Complete
740,001-742,000 - Antonio - Complete
742,001-750,000 - lsoule - Complete
750,001-770,000 - Thomas - Complete
770,001-775,000 - Antonio - Complete
775,001-780,000 - Trilo - Complete
780,001-790,000 - lsoule - Complete (1 prime)
790,001-792,000 - Robert - Complete
792,001-810,000 - lsoule - Complete
810,001-814,000 - Robert - Complete
814,001-840,000 - lsoule - Complete (1 prime)
840,001-842,000 - Robert - Complete
842,001-880,000 - lsoule - Complete
880,001-882,000 - Robert - In Progress
882,001-890,000 - lsoule - Complete
890,001-904,000 - lsoule - Complete
1,000,001-1,030,000 - Batalov - Complete (1 prime)

**Input files** (in the attached 22544.zip file):

22544mi790to800sv_6340B.txt ... pfgw input file in ABC format (790-800k)

22544mi800to1000sv_9600B.txt ... pfgw input file in ABC format (800-1000k)

llr_input_790to1000.txt ... LLR input file in NewPgen format (790-1000k)

llr_input_1030to1200.txt ... LLR input file in NewPgen format (1030-1200k)