20071101, 15:40  #1 
May 2007
Kansas; USA
3^{3}×17×23 Posts 
k*10^n1
Primes of the form k*10^n1 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^n1 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 top5000 site. Here is a link: www.noprimeleftbehind.net/gary/primeskx10n1.htm Eventually I'll update it to include all k's for primes of this form shown on the top5000 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 20090731 at 05:27 
20071107, 15:48  #2  
May 2007
Kansas; USA
3^{3}×17×23 Posts 
Ranges searched for 99*10^n1 and others ?
Quote:
Per an above post, I am maintaining a web page dedicated to primes of the form k*10^n1 since many of them are nearrepeatdigit. To avoid doublework, I am also showing known ranges searched. I've done some 'lowlevel' 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 lowlevel gaps. Would you be able to tell me what range of n you searched for 99*10^n1 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 top5000. 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 top5000 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 

20071107, 16:01  #3 
Mar 2007
179 Posts 
gbarnes017.googlepages.com/primeskx10n1.htm
Hello Gary, What does the (...) nomenclature mean in your tables? Please explain. Thanks,  Rich 
20071107, 16:41  #4 
Feb 2006
Denmark
2×5×23 Posts 
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. 
20071107, 16:46  #5  
May 2007
Kansas; USA
3^{3}×17×23 Posts 
(...) explanation
Quote:
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 doublechecking. 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 top5000 site. It is organized in a similar manner to our www.15k.org pages for k's > 300. Gary 

20071107, 16:59  #6 
Feb 2006
Denmark
E6_{16} 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 20071107 at 17:25 Reason: Adding 6716 
20071107, 17:03  #7  
May 2007
Kansas; USA
10557_{10} Posts 
Quote:
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 nearrepeatdigits. Those being k=2,3,5,6,8,9,92,93,95,96,98,99,992,993,995,...(etc.) Thanks again... Gary 

20071107, 18:46  #8  
May 2007
Kansas; USA
3^{3}×17×23 Posts 
Quote:
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 

20071107, 19:28  #9 
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 nearrepdigit 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. 
20071107, 21:40  #10 
Nov 2003
E26_{16} Posts 
k=995 has one more prime to n=10k at n=9133, tested to 10k long time ago.

20071107, 21:44  #11  
May 2007
Kansas; USA
10100100111101_{2} Posts 
Quote:
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 top5000 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 20071107 at 21:52 
