Choose your own K and work on finding a top-5000 prime!

lsoule · 2005-11-09, 04:15

Below is a list of K values that can be reserved. Each K has at least
90 primes in the range n=0-50k. I have checked the top-5000 list
(as of Jan 2006) and none of these K values have primes reported so
they should be 'clean'.

Code:

       K    # primes  Notes
            n=0-50k

   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=210-770k)
  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=200-255k)
  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 50k-173k)
  1693514745 97   (Reserved by Larry)
  8713308285 96
   317372055 96   (Available, 4 primes reported in n=200-410k)
    19217385 96   (Reserved by nuggetprime)
   146921775 96
   445419975 96   (Reserved by Kosmaj, 7 primes reported in n=200-302k)
   228461805 96   (Reserved by kuratkull)
   317372055 96
   949473525 96
  3289888875 95
  1169473305 95
   776668035 95
    14549535 95   (Reserved by Larry, 3 primes in n=210-290k)
  1062034545 95
  2037910875 95   (Reserved by Larry, 3 primes in n=200-272k)
    80555475 95   (Reserved by Larry, 3 primes in n=200-285k)
    24107655 95   (Available, tested 230-262k with 0 primes)
   174956925 95
   175977945 95
    74784765 95   (Available, tested 230-259k 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=200-400k)
   107337555 94
   828512685 94
   228986175 94
   152751885 93
  2904473715 93   (Reserved by Larry, 7 primes in n=200-370k)
   264766425 93   (Tested to 250k, 2 primes in n=200-250k)
   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=50k-145k)
    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=200-275k)
   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=200-430k)
     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=200-655k)
         465 ??  (Reserved by VBCurtis)
   290499495 ??  (Reserved by gd_barnes)
   968911515 ??  (Reserved by gd_barnes)
   775784295 ??  (Reserved by gd_barnes)
  3428677395 ??  (Reserved by gd_barnes)

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 top-5000 list and run the K in the range 50-100K or more before
embarking on a quest for a top-5000 prime.

To reserve a K, just leave a reply on this forum.

Kosmaj · 2005-11-09, 04:34

Nice table Larry!

One question and two notes

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.

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...

lsoule · 2005-11-09, 05:23

The weight is computed from sieving n=0-10k. 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
low-weight Ks. Those two lists should have many non-15k Ks.

lsoule · 2005-11-09, 06:11

I'll start out with 264766425

Templus · 2005-11-10, 19:05

I'll give 226005 a shot!

NiceMedTexMD · 2005-11-10, 23:21

I'm a little curious as to how this portion works... can someone help me out?

Dr. Mike..

grobie · 2005-11-10, 23:41

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

lsoule · 2005-11-10, 23:45

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 3-4 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 http://www.mersenneforum.org/showthread.php?t=640
Note, the minimum n (nmin in the post) for a top-5000 prime is around
203000 now so I'd start with a range of 203000-250000. 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 0-10k is a reasonable
first guess, but no guarantee. So the strategy may be to run a K in
the n=200-250k range and see how it goes. If no primes result, pick
another K. If you get 2-3 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 top-5000 list.

-Larry

Kosmaj · 2005-11-11, 15:41

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 P-4's then sieve on Athlons, do LLR on P-4's.

Templus · 2005-11-14, 15:44

Sieving in the n=203000 to 300000 range, currently at 125 G and 13800 tests left.

lsoule · 2005-11-19, 05:19

Reserving 80555475

2005-11-10, 23:21	#6
NiceMedTexMD Jun 2004 2×3×7 Posts	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..

2005-11-14, 15:44	#10
Templus Jun 2004 2·53 Posts	update on k=226005 Sieving in the n=203000 to 300000 range, currently at 125 G and 13800 tests left.

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2005-11-09, 04:34	#2
Kosmaj Nov 2003 2·1,811 Posts	Nice table Larry! One question and two notes 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. 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...

2005-11-09, 05:23	#3
lsoule Nov 2004 California 1704₁₀ Posts	The weight is computed from sieving n=0-10k. 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 low-weight Ks. Those two lists should have many non-15k Ks.

2005-11-09, 06:11	#4
lsoule Nov 2004 California 2³×3×71 Posts	I'll start out with 264766425

2005-11-10, 19:05	#5
Templus Jun 2004 2·53 Posts	I'll give 226005 a shot!

2005-11-10, 23:41	#7
grobie Sep 2005 Raleigh, North Carolina 337 Posts	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

2005-11-10, 23:45	#8
lsoule Nov 2004 California 2³×3×71 Posts	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 3-4 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 http://www.mersenneforum.org/showthread.php?t=640 Note, the minimum n (nmin in the post) for a top-5000 prime is around 203000 now so I'd start with a range of 203000-250000. 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 0-10k is a reasonable first guess, but no guarantee. So the strategy may be to run a K in the n=200-250k range and see how it goes. If no primes result, pick another K. If you get 2-3 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 top-5000 list. -Larry

2005-11-11, 15:41	#9
Kosmaj Nov 2003 2×1,811 Posts	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 P-4's then sieve on Athlons, do LLR on P-4's.

2005-11-19, 05:19	#11
lsoule Nov 2004 California 11010101000₂ Posts	Reserving 80555475