Choose your own K and work on finding a too small for top5000 prime!
Below is a list of K values that can be reserved. Each K has at least
90 primes in the range n=050k. I have checked the top5000 list (as of Jan 2006) and none of these K values have primes reported so they should be 'clean'. [CODE] K # primes Notes n=050k 165054615 102 (Reserved by Larry, tested to n=340k, 1 prime reported) 8331405 101 (Reserved by Larry, testing at n=900k) 1501946985 100 (Available) 22932195 99 (Reserved by Larry, 17 primes in n=210770k) 2028893625 98 (Reserved by CedricVonck) 687218805 98 (Reserved by CedricVonck) 1222853775 98 (Available, tested to 348822, 7 primes reported) 1346178405 98 (Reserved by Larry, 1 prime in n=200255k) 1194281385 98 1748348745 98 857996205 98 (Reserved by Larry) 62984955 97 (Reserved by Larry) 1310150985 97 686701125 97 (Tested to n=173307, 19 more primes in 50k173k) 1693514745 97 (Reserved by Larry) 8713308285 96 317372055 96 (Available, 4 primes reported in n=200410k) 19217385 96 (Reserved by nuggetprime) 146921775 96 445419975 96 (Reserved by Kosmaj, 7 primes reported in n=200302k) 228461805 96 (Reserved by kuratkull) 317372055 96 949473525 96 3289888875 95 1169473305 95 776668035 95 14549535 95 (Reserved by Larry, 3 primes in n=210290k) 1062034545 95 2037910875 95 (Reserved by Larry, 3 primes in n=200272k) 80555475 95 (Reserved by Larry, 3 primes in n=200285k) 24107655 95 (Available, tested 230262k with 0 primes) 174956925 95 175977945 95 74784765 95 (Available, tested 230259k with 0 primes) 9158021565 94 2241069285 94 3988569585 94 555567045 94 (Reserved by Edorah, tested to 429k, 10 primes reported) 39418665 94 (Reserved by NiceMedTxMd, 5 primes in n=200400k) 107337555 94 828512685 94 228986175 94 152751885 93 2904473715 93 (Reserved by Larry, 7 primes in n=200370k) 264766425 93 (Tested to 250k, 2 primes in n=200250k) 244133175 93 28397655 93 (Reserved by levitate) 51010245 93 281804985 93 28397655 93 99311355 93 (Reserved by Kar Bon) 96623835 93 1256369595 93 234686595 93 (Available, tested by CedricVonck to n=145k, 9 more primes from n=50k145k) 78290355 93 2481187995 92 8594430075 92 3870706125 92 2641908225 92 1311455145 92 100542585 92 272936235 92 249671565 92 3250995 92 (Tested to n=114832) 1386560175 92 (Reserved by Templus) 105330225 92 384158775 92 44702775 92 199140045 92 240924255 92 226005 91 (Available, tested to n=260k, sieved to 450bn, 1 prime) 8614926705 91 1533677145 91 4259877765 91 759237765 91 (Reserved by Larry, 4 primes in n=200275k) 178140105 91 226231005 91 360949875 91 (Available, tested to n=147627) 35900025 91 8670014925 90 272605245 90 418791945 90 682980375 90 27114615 90 20934375 90 8629569795 89 8858158725 89 719053335 89 11340615 89 19474455 89 4471935 88 (Reserved by NiceMedTxMd) 850612425 88 (Tested to 275965k, 2 primes reported) 5169615 82 (Available. Tested to 430k by amphoria, 8 primes in n=200430k) 7753875 70 up to n=10k (Reserved by NiceMedTxMd, 4 primes reported) 3545685 62 (Reserved by gd_barnes) 692835 60 (Reserved by Larry, 16 primes in n=200655k) 465 ?? (Reserved by VBCurtis) 290499495 ?? (Reserved by gd_barnes) 968911515 ?? (Reserved by gd_barnes) 775784295 ?? (Reserved by gd_barnes) 3428677395 ?? (Reserved by gd_barnes) [/CODE] There are many considerations to picking a K: LLR runs faster on smaller values of K, higher weight K's will have more candidates to test, and luck! You may want to check the most recent top5000 list and run the K in the range 50100K or more before embarking on a quest for a top5000 prime. To reserve a K, just leave a reply on this forum. 
Nice table Larry!
One question and two notes :smile: Q: What range of n is involved in computing the weight? N1: Since we are not 15k anymore we can try k's not divisible by 15. I remember before you mentioned several. In fact from time to time I still work on one of them, k=67773, but I found no reportable primes yet. :sad: N2: There was a program somewhere around to compute Nash/Robinson weights. Just to fill the table but they are not so helpful in finding prolific k's... 
The weight is computed from sieving n=010k. I've updated the original
post with this information. This list takes all 79,000 candidates I tested and sorted them by total number of primes. These all happen to be 15k. I also plan on posting lists for # primes/candidates and lowweight Ks. Those two lists should have many non15k Ks. 
I'll start out with 264766425

I'll give 226005 a shot! :smile:

How do I give this portion a shot?
I'm a little curious as to how this portion works... can someone help me out?
Dr. Mike.. 
Hey everyone!
I like your table Larry. I think someone needs to set up a getting started link for new members, so they will know what programs to use & how to use them. Later grobie  Tony 
Sure thing! In the new RPS team drive and other group activities,
we have done the K selection and sieving for you. All you have to do is run LLR. If you want to venture out into testing your own K, you can select one here, sieve it, then run LLR yourself. It all depends on how you want to work. The group searches are usually split up into chunks of 34 days of work. If you run your own K and find a productive one, you may stick with that one for months reporting primes along the way. Basically, less communication is needed and you have more 'control'. For details on how to sieve and run LLR, you can see the post in the 15k forum at [url]http://www.mersenneforum.org/showthread.php?t=640[/url] Note, the minimum n (nmin in the post) for a top5000 prime is around 203000 now so I'd start with a range of 203000250000. For the Ks listed here, I would expect, *on average*, about 2 primes to be in that range. The 'on average' meaning that the productivity of a certain K isn't really known. Measuring the number of primes in the range 010k is a reasonable first guess, but no guarantee. So the strategy may be to run a K in the n=200250k range and see how it goes. If no primes result, pick another K. If you get 23 primes, you will probably want to continue on in the 250k+ range. Of course, the larger the prime, the longer it'll stick around on the top5000 list. Larry 
I found the weight for k=698790798615 to be 1937.
When k>2^31 it has to be given to NewPGen as a product of factors less than 2^31. In the example above, k=1763*396364605. If such factorization does't exist then such k cannot be sieved using NewPgen. Also, when using NewPGen be sure to check the "Verify results" box. There were reports of wrong results if it's not checked. I also log the removed numbers (Options>Log the numbers removed). And finally, sieve agressively, to say so, 24 hrs sieving is not enough (except for some very low weight k's or very small ranges of n). In my experience you cannot oversieve if you go to 1T (1000 bn), not even to 2T. If you have both Athlons and P4's then sieve on Athlons, do LLR on P4's. 
update on k=226005
Sieving in the n=203000 to 300000 range, currently at 125 G and 13800 tests left.

Reserving 80555475

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