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Old 2005-12-17, 14:53   #1
ppo
 
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Default big factor reported

is this:
Code:
30867071 102   F  3953901635355166087069060014031  17-Dec-05 00:55  koekie         melig
the biggest factor reported on the server ?
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Old 2005-12-17, 18:45   #2
alpertron
 
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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 102-bit prime.

Some people here can compute the probability that the algorithm p-1 can find a prime with 102 or more bits given that p-1 is multiple of 30867071.
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Old 2005-12-18, 21:12   #3
ewmayer
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p-1 factors of over 100 bits are not terribly rare - I remember seeing the 113-bit factor 9859882222392454186560939051870161 of M20812849, and there may be even larger ones. Still nice to find, though. ;)
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Old 2006-01-01, 22:03   #4
Paulie
 
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Quote:
Originally Posted by ppo
is this:
Code:
30867071 102   F  3953901635355166087069060014031  17-Dec-05 00:55  koekie         melig
the biggest factor reported on the server ?

I found this one a while ago:

23292847 F 103 8092687948661261082412157958831 14-Feb-04 01:24 PJM-Borg01

Code:
8092687948661261082412157958831
Sieving...
3 * 7 * 
Commencing Pollard rho...
...
92507
* 
Commencing Pollard (p-1)...
..
102103
* 40800022252112594591

Last fiddled with by Paulie on 2006-01-01 at 22:04
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Old 2006-02-13, 20:12   #5
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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)
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Old 2006-02-13, 20:26   #6
Paulie
 
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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.
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Old 2006-02-13, 21:48   #7
Prime95
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Quote:
Originally Posted by Paulie
I found this one a while ago:

23292847 F 103 8092687948661261082412157958831 14-Feb-04 01:24 PJM-Borg01
You cannot trust any factors reported as 102 bits or larger on the PrimeNet reports. These are probably the last 32 characters of a factor that is more than 102 bits.
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Old 2006-02-14, 17:38   #8
ewmayer
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Quote:
Originally Posted by Prime95
You cannot trust any factors reported as 102 bits or larger on the PrimeNet reports. These are probably the last 32 characters of a factor that is more than 102 bits.
Indeed, in gathering sample large p-1 factors for the self-test suite of my Mfactor code module, I wrote some special debug code to take such partial factors and reconstruct the missing upper digits (up to some reasonable size bound).
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Old 2006-02-15, 11:26   #9
Greenbank
 
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Add a 1 on the front.

2^23292847-1 mod 18092687948661261082412157958831 = 0

So it is 103 bits.
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Old 2006-02-16, 22:05   #10
Paulie
 
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Thanks Greenbank.
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Old 2006-03-18, 20:56   #11
James Heinrich
 
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The top-10 reported P-1 factors on the Mersenne-aries stats page are all more than 30 decimal digits:
http://mersenne-aries.sili.net/?showuserstats=*

My longest is 4323110550526375709294437681284209923347881 for M15910439
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