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 2007-11-01, 15:40 #1 gd_barnes     May 2007 Kansas; USA 25·331 Posts k*10^n-1 Primes of the form k*10^n-1 are kind of a fun diversion from my usual Riesel prime searches because many of them are near repeat digit primes. A near repeat digit prime is one where all of its digits are the same except for one. I searched 2*10^n-1 up to n=10K. That is all I've searched for now because they take much longer to search than Riesels. But I have created a web page that lists primes of this form for all k<100 that are currently stored on the top-5000 site. Here is a link: www.noprimeleftbehind.net/gary/primes-kx10n-1.htm Eventually I'll update it to include all k's for primes of this form shown on the top-5000 site and do a little more searching at low ranges after a couple of my current efforts are finished. Gary Last fiddled with by amphoria on 2009-07-31 at 05:27
2007-11-07, 15:48   #2
gd_barnes

May 2007
Kansas; USA

296016 Posts
Ranges searched for 99*10^n-1 and others ?

Quote:
 Originally Posted by lsoule Earlier this month I found 99*10^139670-1, the new Near-repdigit record. In fact, 10 of the top 20 for this form have been entered in the last 2-3 months.
Larry, congratulations on a nice record that still stands!

Per an above post, I am maintaining a web page dedicated to primes of the form k*10^n-1 since many of them are near-repeat-digit. To avoid double-work, I am also showing known ranges searched. I've done some 'low-level' searching on k=2, 3, & 5 to 'fill in some gaps' up to at least n=10K and have gotten some info. from another site for k < 10 that appears to fill in more low-level gaps.

Would you be able to tell me what range of n you searched for 99*10^n-1 to obtain this record? Also, if you searched any other k's, would you have any searched range info. on those?

The site that I found that helps fill in some gaps for k < 10 is here: homepage2.nifty.com/m_kamada/math/factorizations.htm
It has info for all k's < 10 for all n < 200 and then some additional primes up to and including what is on top-5000. It's not much help...it only really fills in gaps for n<~5K but doesn't show specific ranges searched, although it is an interesting site.

My web page includes my small searches plus info. from the above web site plus top-5000 info.

If anyone knows of any more web sites for this form that have add'l. info., I'll add it to my page.

Thanks,
Gary

 2007-11-07, 16:01 #3 monst     Mar 2007 179 Posts gbarnes017.googlepages.com/primes-kx10n-1.htm Hello Gary, What does the (...) nomenclature mean in your tables? Please explain. Thanks, -- Rich
2007-11-07, 16:41   #4
Jens K Andersen

Feb 2006
Denmark

2×5×23 Posts

Quote:
 Originally Posted by monst What does the (...) nomenclature mean
Comparing to "range of n tested" shows that it means end of the known exhaustive tests, so there could be missing n's after (...)

http://www.research.att.com/~njas/sequences/A111391 gives these n for k=11:
1, 9, 11, 17, 22, 29, 36, 37, 52, 166, 448, 2011, 3489, 4871, 6982

I computed the first n values for k < 50 with no k line in Gary's table, and then searched those n in OEIS. Only the above k=11 was found.

2007-11-07, 16:46   #5
gd_barnes

May 2007
Kansas; USA

1059210 Posts
(...) explanation

Quote:
 Originally Posted by monst gbarnes017.googlepages.com/primes-kx10n-1.htm Hello Gary, What does the (...) nomenclature mean in your tables? Please explain. Thanks, -- Rich
Thanks for your interest, Rich.

It means that the max n consecutively tested is somewhere between the 2 prime n's shown. See the 'range of n tested' column. For example for k=2, testing is complete to n=20k so there is a (...) between primes at n=19233 and 38232.

It also means that there is a possible 'gap' in testing. The ranges above the (...) need to be tested to see if there are additional primes. Therefore any additional info. that I can get about ranges searched avoids double-checking.

The testing was either done by me or was obtained from the 'kamada' site shown above. It is not known what ranges were searched for primes obtained from the top-5000 site.

It is organized in a similar manner to our www.15k.org pages for k's > 300.

Gary

 2007-11-07, 16:59 #6 Jens K Andersen     Feb 2006 Denmark 23010 Posts k=455 gives 25 primes for n < 5000: 1, 7, 11, 12, 13, 17, 24, 25, 38, 47, 49, 54, 65, 74, 96, 104, 120, 295, 379, 874, 1488, 1667, 2717, 3585, 3851 And n=6716 after testing to 7000. Last fiddled with by Jens K Andersen on 2007-11-07 at 17:25 Reason: Adding 6716
2007-11-07, 17:03   #7
gd_barnes

May 2007
Kansas; USA

25×331 Posts

Quote:
 Originally Posted by Jens K Andersen Comparing to "range of n tested" shows that it means end of the known exhaustive tests, so there could be missing n's after (...) http://www.research.att.com/~njas/sequences/A111391 gives these n for k=11: 1, 9, 11, 17, 22, 29, 36, 37, 52, 166, 448, 2011, 3489, 4871, 6982 I computed the first n values for k < 50 with no k line in Gary's table, and then searched those n in OEIS. Only the above k=11 was found.
Ah, the most excellently organized 'integer sequences' site! Thanks for the info. I will update my page for k=11. It's interesting that the site showed the form as 10^(n+1)+(10^n-1) even though 11*10^n-1 is a simpler form of the equation.

That was a good idea to get the first few primes and then search the integer sequences site for them. I may try that for some more k's since it takes little time.

I will only show k=11 tested up to n=50 since you stated that is what you did. (You stated n<50 but I checked n=50 and it has a factor of 7.) We have no way to know for sure if the person who sent the info. to the integer sequences site tested all of the n.

One more thought...I want any and all info. for this form but I'm most interested in k's that make the numbers near-repeat-digits. Those being k=2,3,5,6,8,9,92,93,95,96,98,99,992,993,995,...(etc.)

Thanks again...
Gary

2007-11-07, 18:46   #8
gd_barnes

May 2007
Kansas; USA

25×331 Posts

Quote:
 Originally Posted by Jens K Andersen k=455 gives 25 primes for n < 5000: 1, 7, 11, 12, 13, 17, 24, 25, 38, 47, 49, 54, 65, 74, 96, 104, 120, 295, 379, 874, 1488, 1667, 2717, 3585, 3851 And n=6716 after testing to 7000.
Jens,

Excellent! Thanks for the contribution. I have now added k=11 and k=455 to the web page.

And in a stroke of luck, on the 'integer sequences' site, they show the range of n that was used in the program 'Mathematica' to obtain the sequences that they show. Being a very trusted source of information, I was able to use it and show the ranges tested for k=6, 8, 9, and 11 up to at least n=3K. The ones for k=2, 3, and 5 weren't as high as I had tested.

At the bottom of the page, I also added the 3 sites where the original info. was obtained from and listed you as a contributor.

Thanks,
Gary

 2007-11-07, 19:28 #9 Jens K Andersen     Feb 2006 Denmark 2×5×23 Posts k=455 is also prime for n=9542. Search stopped at 10000. k=81066 gives 30 primes for n <= 5000: 1, 2, 6, 10, 12, 16, 19, 24, 32, 34, 36, 41, 66, 86, 91, 124, 152, 176, 305, 562, 568, 838, 980, 986, 1217, 1452, 1646, 1692, 1847, 2386 k=995 gives 23 near-repdigit primes for n<=7000: 1, 8, 9, 13, 15, 20, 21, 23, 81, 100, 112, 262, 327, 407, 481, 745, 1216, 1804, 1909, 4317, 5896, 6469, 6537 By the way, my name is Andersen and not Anderson.
 2007-11-07, 21:40 #10 Kosmaj     Nov 2003 2·1,811 Posts k=995 has one more prime to n=10k at n=9133, tested to 10k long time ago.
2007-11-07, 21:44   #11
gd_barnes

May 2007
Kansas; USA

25·331 Posts

Quote:
 Originally Posted by Jens K Andersen k=455 is also prime for n=9542. Search stopped at 10000. k=81066 gives 30 primes for n <= 5000: 1, 2, 6, 10, 12, 16, 19, 24, 32, 34, 36, 41, 66, 86, 91, 124, 152, 176, 305, 562, 568, 838, 980, 986, 1217, 1452, 1646, 1692, 1847, 2386 k=995 gives 23 near-repdigit primes for n<=7000: 1, 8, 9, 13, 15, 20, 21, 23, 81, 100, 112, 262, 327, 407, 481, 745, 1216, 1804, 1909, 4317, 5896, 6469, 6537 By the way, my name is Andersen and not Anderson.

It's now been updated. Sorry about the misspelling. It's now corrected. That's a nice k=81066 with 30 primes for n<=5000.

A couple of questions:
1. Did you have a method that you used to come up with a k that produced a lot of primes? I don't know if the Nash Weight software can do bases other than 2.

2. What software are you using for testing? I've sieved with sr1sieve and then used LLR for primality testing to find probable primes. I then follow up and prove primality with Proth. But I'm open to any faster way of doing things.

I think I'm going to fill in some low gaps for n<5000 for some of the old top-5000 k's using just Proth only.

Edit: Kosmaj, I just now saw your prime and range and added it plus you as a contributor.

Thanks again,
Gary

Last fiddled with by gd_barnes on 2007-11-07 at 21:52

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