20160511, 06:37  #1 
"NOT A TROLL"
Mar 2016
California
11000101_{2} Posts 
Very (large) PRPs?
I was reading this list, when I found out it wasn't too hard to find all those PRPs. I looked at the end of the list, and found that "random" PRPs are discovered with 50,000 digits. What should I best use to find "random" PRPs say between 50k and 200k digits? Not that I would want to ever submit them on the PRPtop because the site simply does not accept "random" PRPs and there are no such PRPs there either. I would expect this to be done in about a week too, (200k digits almost), but correct me if that is not possible, please.

20160511, 06:53  #2 
Romulan Interpreter
Jun 2011
Thailand
9154_{10} Posts 
The "list" will accept "random" PRPs. Find one with more than 46k digits and send it there. Just find one.

20160511, 08:58  #3  
Jun 2003
3·5·17·19 Posts 
The submission page lists 20,000 digit as the minimum. But to actually enter Top 10000, it should be 42k+.
The submission page also says that Quote:


20160511, 16:52  #4 
"NOT A TROLL"
Mar 2016
California
197_{10} Posts 
Can you find any examples of "random" PRPs on the site? I was looking for a specific program that I could input the large number in a .txt file (about 200,000 digits) and call nextprime(x) or previousprime(x), Pfgw is too slow is my guess?

20160511, 18:45  #5  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
59·157 Posts 
Quote:
nextprime(10^x) (and next and next and next) nextprime(12^x) some other random example Finding one is very easy, if that's your goal or if you find it fun thing to do. Most contributors there don't stop until they submit tens of thousands. 

20160511, 23:17  #6 
"NOT A TROLL"
Mar 2016
California
197 Posts 
First, with what text editor can carry 200k+digits (need at least 400k digits) so I can input into pfgw (or some other program which can give me a direct result regardless the size for nextprime(x) = ?):
input.txt:  nextprime(597612129456797651389670218204770656.........(199,928 more digits).........107345799455301271768055018207593331)597612129456797651389670218204770656.........(199,928 more digits).........107345799455301271768055018207593331  And get a result like this f i input.txt nextprime(x)x is a 3PRP! t q input.txt nextprime(597612129456797651389670218204770656.........(199,928 more digits).........107345799455301271768055018207593331) is a Fermat and Lucus PRP! I don't want to risk notepad, but someone who has tried that please let me know. Pfgw output I do nextprime(x)x, but when i input nextprime(x) it gives me: nextprime(x) is a 3PRP! So I do not know what nextprime(x) is, but I can ignore that using nextprime(x)x. Last fiddled with by PawnProver44 on 20160511 at 23:21 
20160511, 23:26  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9263_{10} Posts 

20160512, 11:45  #8 
Aug 2002
Buenos Aires, Argentina
3^{2}×149 Posts 

20160512, 16:53  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010000101111_{2} Posts 
Good point! I lost a "+" in the message: it is a billion+ digit number and qualifies for the EFF prize not!

20160512, 20:53  #10 
"NOT A TROLL"
Mar 2016
California
197 Posts 
Here are my running times with Wolfram  Alpha? (random 10, 20, 40, 80 digit numbers) Can anyone compare to Pfgw to see if it is faster?
nextprime(1615940397) = 1615940399 (1.2 s) nextprime(14068924638939642180) = 14068924638939642181 (1.3 s) nextprime(3718587170008038384873784221963098409550) = 3718587170008038384873784221963098409563 (1.3 s) nextprime(97783010505674166402735696905325823805408510851148150244960782744188145048695585) = 97783010505674166402735696905325823805408510851148150244960782744188145048695591 (1.3 s) I was expecting the time to be at lest 16 times as much for doubling the number of digits? Is this true for Pfgw? Thanks to anyone who can give approximate running times for Pfgw for (1,000; 2,000; 4,000; 8,000; digits PRPs please) as a larger version of my test. Edit: I forgot to call nextprime(x) for random 80 digit number. Last fiddled with by PawnProver44 on 20160512 at 21:04 
20160512, 21:05  #11  
Aug 2002
Buenos Aires, Argentina
3^{2}×149 Posts 
Quote:
Last fiddled with by alpertron on 20160512 at 21:07 

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