20130906, 16:33  #166 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2·283 Posts 
I don't know if it will be all wrong if we include:
if so the list would also include proven PRPs and primes/PRPs for k:s which are not 0 or 1 (mod 4). Would that be OK? So far the above would be the only addition I guess. Last fiddled with by aketilander on 20130906 at 16:36 
20130906, 16:35  #167  
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×3×5×7×47 Posts 
Quote:
Quote:
Last fiddled with by LaurV on 20130906 at 16:41 

20130906, 17:45  #168  
Banned
"Luigi"
Aug 2002
Team Italia
2·41·59 Posts 
Quote:
Now the history is updated. BTW, you did a terrific job!! I guessed you used PARI and pfgw for your search. Luigi Last fiddled with by ET_ on 20130906 at 17:47 Reason: History updateed. 

20140110, 20:34  #169 
Banned
"Luigi"
Aug 2002
Team Italia
11346_{8} Posts 
2*140340*(2^12577871)+1 is prime!
A new, 378,638digits prime has been found and proved.
Sadly, it doesn't divide MM34. Luigi 
20140110, 22:14  #170 
"Phil"
Sep 2002
Tracktown, U.S.A.
1119_{10} Posts 

20140111, 12:27  #171 
Einyen
Dec 2003
Denmark
3·5·7·31 Posts 
Very nice! It is not a PRP?
Which software proves these numbers prime when they are on of the form k*2^(p+1) 2k+1 ? 
20140111, 13:34  #172  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4,271 Posts 
Quote:
2^12577871 is prime (and 140340 is trivially factored) Thus, N1's factorization is known. So I'd go with an N1 test for proving. Nice find! Last fiddled with by MiniGeek on 20140111 at 13:35 

20140111, 13:42  #173  
Banned
"Luigi"
Aug 2002
Team Italia
1001011100110_{2} Posts 
Quote:
I also aplied the GwPowMod function via a pfgw script to check that the factor was not a divisor of MM34. Luigi 

20140111, 17:54  #174 
Einyen
Dec 2003
Denmark
110010110111_{2} Posts 
Did you use pfgw? How long did N1 test take? and how long to test if factor of MM34?
Does pfgw or whatever software you use have to test 2^12577871 for primality first or can you specify, that you know it is prime? 
20140111, 18:55  #175  
Banned
"Luigi"
Aug 2002
Team Italia
2·41·59 Posts 
Quote:
N1 took less than 8000 seconds. GwPowMod was about 4 times faster. MM34 was given as a known prime factor of N1 from an helper file, for the calculation. It wasn't that hard, after all... the hard work is to sieve all the possible ks, PRP the candidates and testing for primality was just the tip of the iceberg. Many thanks to Serge Batalov who tested all the survived Ks of MM34 (and many, many others) up to 130,000. Now, looking at the status it seems that MM36 was left behind... anyone willing to give a pfgw shot to it? If you find a PRP you may add a 900,000 digits long prime to your curriculum. Note: the prime in fulldigits' size is available here. Luigi Last fiddled with by ET_ on 20140111 at 18:57 Reason: Added a link. 

20140210, 12:11  #176 
Banned
"Luigi"
Aug 2002
Team Italia
2×41×59 Posts 
DoubleMersennes.org strikes again!
2*9488*(2^29762211)+1 is prime!
This 895,937 digits number has been proved prime; rankes #113 among the biggest primes of all times, is actually being tested by Chris Caldwell site. It doesn't divide MM36, though. We're getting closer and closer to the first milliondigits prime for double Mersennes possible factors. Luigi 
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