20160715, 06:38  #177 
May 2004
New York City
4232_{10} Posts 
It's a kinda cool race which I'm enjoying from
the grandstands of my home PC (HP 64bit Windows 10). What's the ET2CU (estimated time to catch up) for the OP a(20) now past 500k versus pi(0,314): 314159265358979323846...89830932080370010789 (613373 digits) Lucas PRP! (70233.3140s+30.6992s) ?? 
20161010, 14:41  #178 
May 2004
New York City
2^{3}×23^{2} Posts 
No activity here in a while. Has a(20) reached a milestone yet?
When it reaches 700000 (or 1000000) I think it would be cause to pause for some kind of NT analysis...is it seriously possible for the a(20) series to have NO primes...if so, is this a unique instance in pi...are there other related implications. 
20161010, 18:15  #179  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{8}·41 Posts 
This thread was started so long ago that I had to review its start to understand what's going on. I came across the following:
Quote:
To expand a little: normality to base a means that all possible strings containing the digits of a occur somewhere in the basea expansion of pi. In particular, all possible decimal primes are hypothesized to be contained somewhere in the decimal expansion of pi. The problem is finding them. I'm sure that Serge's analysis is correct. I haven't yet proved under the normality conjecture that his red sequence does NOT contain a prime if continued far enough. 

20161010, 20:36  #180  
"Mark"
Apr 2003
Between here and the
6,163 Posts 
Quote:
Quote:


20161010, 20:44  #181  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{8}×41 Posts 
Quote:
I really have no idea whether the proposition is true, false or undecidable. 

20161012, 19:18  #182 
Sep 2013
2^{3}×7 Posts 
With the help of pixsieve (thanks again, rogue!) and
a new 6600K its now 57x faster than my old machine. Enthusiasm rekindled, chugging along. #20 is approaching 600K and the other 8 unfinished up to 1666 are between 250K and 300K. 
20161016, 13:23  #183 
Sep 2013
2^{3}·7 Posts 
First hit with the new machinery.
#861, 279430 digits PRP. 
20170117, 22:46  #184  
Einyen
Dec 2003
Denmark
5677_{8} Posts 
Quote:
I checked all the way up to this prime and up to 650K without finding any other primes. Here are factors up to 1,000,000 digits sieved to 134G (including a few ECM factors): pifactors.txt Ignoring all the even numbers and those ending in 5 and removing these factors and known primes leaves these candidates (I didn't remove the new 613373 digit prime): remaining.txt Here are pfgw logs from running these up to 650K, use http://7zip.org/ to unpack them even though they are called ".zip". 000k100k.zip (139 KB, unpacks to 104 MB) 100k200k.zip (297 KB, unpacks to 316 MB) 200k300k.zip (532 KB, unpacks to 540 MB) 300k350k.zip (389 KB, unpacks to 342 MB) 350k400k.zip (439 KB, unpacks to 399 MB) 400k450k.zip (487 KB, unpacks to 449 MB) 450k500k.zip (538 KB, unpacks to 512 MB) 500k550k.zip (823 KB, unpacks to 567 MB) 550k600k.zip (889 KB, unpacks to 609 MB) 600k650k.zip (965 KB, unpacks to 702 MB) 

20170320, 20:22  #185 
May 2004
New York City
2^{3}×23^{2} Posts 
A large prime in the digits of pi is interesting, although except for the unusual
magnitude I don't see right off how it may be numbertheoretically important. Perhaps there's a finite significant collection of outofproportionallylarge such primes whose numeric values combined in some way might lead to a theorem? Musing... If there had been an actual prime gap at a(20), and I don't say how that might have been proven, I think that might have been more significant, since the number of such prime gaps might be finite. 
20170320, 20:40  #186 
"Mark"
Apr 2003
Between here and the
14023_{8} Posts 
Aren't most primes that people search for unimportant? Maybe someone should start a "why I search for primes" thread.

20170320, 21:24  #187 
"Curtis"
Feb 2005
Riverside, CA
3×5×307 Posts 
perhaps davar55 ought to define "important" from his viewpoint, so we can know which projects he finds unimportant.

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