20051217, 14:53  #1 
Aug 2004
italy
113 Posts 
big factor reported
is this:
Code:
30867071 102 F 3953901635355166087069060014031 17Dec05 00:55 koekie melig 
20051217, 18:45  #2 
Aug 2002
Buenos Aires, Argentina
2^{2}×3×113 Posts 
This can be explained because p  1 = 2 x 3 x 5 x 23 ^ 2 x 43 x 109 x 269 x 467 x 62119 x 220681 x 30867071.
The latest prime factor is always a divisor of M(30867071), so it does not count for the "smoothness" of the number. The number 62119 must be less than the bound B1 and 220681 must be less than the bound B2. From this LMH thread for exponents about 20M the value of B1 is 120000 and the value of B2 is 2430000. For exponents near 30M the bounds must be greater (but I don't have the exact numbers Prime95 is using), so Prime95 was able to find this 102bit prime. Some people here can compute the probability that the algorithm p1 can find a prime with 102 or more bits given that p1 is multiple of 30867071. 
20051218, 21:12  #3 
∂^{2}ω=0
Sep 2002
República de California
26560_{8} Posts 
p1 factors of over 100 bits are not terribly rare  I remember seeing the 113bit factor 9859882222392454186560939051870161 of M20812849, and there may be even larger ones. Still nice to find, though. ;)

20060101, 22:03  #4  
Aug 2002
223 Posts 
Quote:
I found this one a while ago: 23292847 F 103 8092687948661261082412157958831 14Feb04 01:24 PJMBorg01 Code:
8092687948661261082412157958831 Sieving... 3 * 7 * Commencing Pollard rho... ... 92507 * Commencing Pollard (p1)... .. 102103 * 40800022252112594591 Last fiddled with by Paulie on 20060101 at 22:04 

20060213, 20:12  #5 
Jan 2003
Altitude>12,500 MSL
101 Posts 
Paulie, the v5 factor checker under test now says:
8092687948661261082412157958831 is NOT factor of M(23292847) but: 3953901635355166087069060014031 IS FACTOR of M(30867071) 9859882222392454186560939051870161 IS FACTOR of M(20812849) 
20060213, 20:26  #6 
Aug 2002
337_{8} Posts 
Saw that, posed in the other thread. It passed on the old server.
Aw man, I don't want to lose credit from my biggest returned factor! I hope it's the new code. 
20060213, 21:48  #7  
P90 years forever!
Aug 2002
Yeehaw, FL
2^{2}·1,873 Posts 
Quote:


20060214, 17:38  #8  
∂^{2}ω=0
Sep 2002
República de California
2D70_{16} Posts 
Quote:


20060215, 11:26  #9 
Jul 2005
110000010_{2} Posts 
Add a 1 on the front.
2^232928471 mod 18092687948661261082412157958831 = 0 So it is 103 bits. 
20060216, 22:05  #10 
Aug 2002
223_{10} Posts 
Thanks Greenbank.

20060318, 20:56  #11 
"James Heinrich"
May 2004
exNorthern Ontario
2×41^{2} Posts 
The top10 reported P1 factors on the Mersennearies stats page are all more than 30 decimal digits:
http://mersennearies.sili.net/?showuserstats=* My longest is 4323110550526375709294437681284209923347881 for M15910439 
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