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 2021-08-20, 07:32 #1 Cybertronic     Jan 2007 Germany 1A516 Posts new prime k-tuplet page Hello members ! Tony Forbes told me, from sep. 21 is the old "prime k-tuplet" page frozen by google. He ask me for taking over his work. Yes, today I bought a new domain. I will try to carry on his layout. New link: www.pzktupel.de\ktuplets.htm So all future results or records to me. best wishes Norman
 2021-08-20, 09:10 #2 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 24·613 Posts Nice one, good luck! A small observation, the term "first appearance", used a lot there, is somehow confuse (and misleading), for sure most of those are not "first appearances" (i.e. there are a lot of smaller primes of the same size, for almost all those in the tables). It seems you use the term as the earliest date of discovery, or something. All those cases should bear an asterisk or footnote saying so. Last fiddled with by LaurV on 2021-08-20 at 09:12
 2021-08-20, 10:37 #3 Cybertronic     Jan 2007 Germany 1101001012 Posts first appearances You mean "first known appearances" is better ? "first appearances" is take over
 2021-08-20, 12:13 #4 rogue     "Mark" Apr 2003 Between here and the 2·5·647 Posts Could you add details on software that can be used (and how to use it) for finding tuplets? I think that many people would be interested in finding new records. A few might actually be interested in improving the speed of the software used to find them.
2021-08-21, 11:21   #5
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

100110010100002 Posts

Quote:
 Originally Posted by Cybertronic You mean "first known appearances" is better ? "first appearances" is take over
No, I mean it should say like "sorted by the time of discovery" or something. Some native English speaker can weight in better than me. For example, for 100 digits, there are lots and lots of primes smaller than 2^521-1. That can not be "first apparition". Even for 157 digits itself, this is not the "first appearance", that should be 10^156+451, which can be found in 10 milliseconds with pari (type: nextprime(10^156)). Maybe it was the earliest discovered, but that's also arguable. The "first apparition" of twin primes of 100+x digits, for x=0 to 9 can be found very fast with nowadays computers, the next script runs just 7 seconds for 100 to 110, single core (and similar, for larger tuples, for so low digits count), so it would not take too long to solve the "unreliable" part of the tables. What is "unreliable" about??

Code:
firstTwins(fromDigit=1, toDigit=200)=
{
for(n=0,toDigit-fromDigit,
q=1;
forprime(p=10^(fromDigit+n-1),10^(fromDigit+n),
if(p-q == 2,
if(q == 3,
print("Found 1 digit: 10^0+3 + {0,2}"),
print("Found "fromDigit+n" digits: 10^"fromDigit+n-1"+"q-10^(fromDigit+n-1)" + {0,2}")
);
break
);
q = p
)
);
}

gp > firstTwins(100,110)
Found 100 digits: 10^99+6001 + {0,2}
Found 101 digits: 10^100+35737 + {0,2}
Found 102 digits: 10^101+139201 + {0,2}
Found 103 digits: 10^102+106759 + {0,2}
Found 104 digits: 10^103+29659 + {0,2}
Found 105 digits: 10^104+3457 + {0,2}
Found 106 digits: 10^105+113617 + {0,2}
Found 107 digits: 10^106+94789 + {0,2}
Found 108 digits: 10^107+52819 + {0,2}
Found 109 digits: 10^108+66517 + {0,2}
Found 110 digits: 10^109+35371 + {0,2}
gp > ##
***   last result computed in 6,876 ms.
gp > nextprime(10^156)-10^156
%  =  451
gp > firstTwins(157,157)
Found 157 digits: 10^156+10489 + {0,2}
gp >

Last fiddled with by LaurV on 2021-08-21 at 11:27

2021-08-21, 11:40   #6
mart_r

Dec 2008
you know...around...

3·229 Posts

Gute Arbeit!

Quote:
 Originally Posted by Cybertronic You mean "first known appearances" is better ? "first appearances" is take over
I'd vote for "earliest discovery of 100 (1000 etc.) digits".
Then you may add "first appearances of ... digits", as you have also calculated them, as well, maybe with a link to your detailed list "smallest-n-digit-prime-k-tuplets".

2021-08-22, 09:34   #7
Cybertronic

Jan 2007
Germany

421 Posts

Quote:
 Originally Posted by mart_r Gute Arbeit! I'd vote for "earliest discovery of 100 (1000 etc.) digits". Then you may add "first appearances of ... digits", as you have also calculated them, as well, maybe with a link to your detailed list "smallest-n-digit-prime-k-tuplets".

I will not change the wording of T. Forbes, but I have extended under "27." a link to the smallest k-tuplet session.
http://www.pzktupel.de/ktuplets

BTW, today I found the second kind of "smallest googol prime 10-tuplet". So the pair is now known.

 2021-08-25, 19:44 #8 Cybertronic     Jan 2007 Germany 421 Posts Early discovery Okay, I changed it now into "Early discovery" and took other colors. http://www.pzktupel.de/ktuplets I hope it is correct now. Norman
 2021-08-27, 04:24 #9 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 24×613 Posts Nice. I love the "smallest tuples" list, the only observation is that you should put the "last updated" text at the beginning, and not at the end. That's for us, so you won't force the reader to go to the end (when I open the page I should see immediately if there was any update, and don't waste my time), but also for you so you won't forget changing the date when you make updates, hihi (the 2012 can't be right as long as you have tuples discovered in 2013, 2014, etc). Last fiddled with by LaurV on 2021-08-27 at 04:25
 2021-08-27, 08:53 #10 Cybertronic     Jan 2007 Germany 421 Posts >> "last updated" text at the beginning, and not at the end. >> the 2012 can't be right... @LaurV Where exactly ?
 2021-08-27, 09:30 #11 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 24·613 Posts See? Told you! It is difficult to find even for yourself (I just searched for "smallest" to find it again) Here, linked from here, section 23, "Odds and Ends". (I didn't go through all the site yet, but that will come, trust me, hehe). And as we spoke of it, maybe you can add section links, you know, "#-something" like wiki has, so we don't need to specify the section and chapter when we talk about it. -scratch that, you have that already, but I am silly. Very good work! Last fiddled with by LaurV on 2021-08-27 at 09:36

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