big factor reported

ppo · 2005-12-17, 14:53

is this:

Code:

30867071 102   F  3953901635355166087069060014031  17-Dec-05 00:55  koekie         melig

the biggest factor reported on the server ?

alpertron · 2005-12-17, 18:45

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.

ewmayer · 2005-12-18, 21:12

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. ;)

Paulie · 2006-01-01, 22:03

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

Old man PrimeNet · 2006-02-13, 20:12

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)

Paulie · 2006-02-13, 20:26

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.

Prime95 · 2006-02-13, 21:48

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.

ewmayer · 2006-02-14, 17:38

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).

Greenbank · 2006-02-15, 11:26

Add a 1 on the front.

2^23292847-1 mod 18092687948661261082412157958831 = 0

So it is 103 bits.

Paulie · 2006-02-16, 22:05

Thanks Greenbank.

James Heinrich · 2006-03-18, 20:56

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

2005-12-17, 14:53	#1
ppo Aug 2004 italy 113 Posts	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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2005-12-17, 18:45	#2
alpertron Aug 2002 Buenos Aires, Argentina 2476₈ 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 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.

2005-12-18, 21:12	#3
ewmayer ∂²ω=0 Sep 2002 República de California 2·7·829 Posts	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. ;)

2006-02-13, 20:12	#5
Old man PrimeNet 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)

2006-02-13, 20:26	#6
Paulie Aug 2002 223 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.

2006-02-15, 11:26	#9
Greenbank Jul 2005 110000010₂ Posts	Add a 1 on the front. 2^23292847-1 mod 18092687948661261082412157958831 = 0 So it is 103 bits.

2006-02-16, 22:05	#10
Paulie Aug 2002 223 Posts	Thanks Greenbank.

2006-03-18, 20:56	#11
James Heinrich "James Heinrich" May 2004 ex-Northern Ontario 6300₈ Posts	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