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2012-10-05, 17:51   #551
TObject

Feb 2012

34·5 Posts

Quote:
 Originally Posted by ET_ A math book on Mersenne factors? 85 has not the form 2kp+1... and 268435456 is 228 and not prime. Luigi
Did whoever created the ECM Progress report on PrimeNet also win the said book? LOL

 2012-10-05, 18:52 #552 c10ck3r     Aug 2010 Kansas 547 Posts Composite exponent + composite divisor= ?
2012-10-06, 04:02   #553
axn

Jun 2003

32×19×29 Posts

Quote:
 Originally Posted by TObject Did whoever created the ECM Progress report on PrimeNet also win the said book? LOL
Quote:
 Originally Posted by FTFP ECM on Fermat numbers
Fermat number = 2^xxxx+1

Last fiddled with by axn on 2012-10-06 at 04:03

 2012-10-09, 00:39 #554 Jwb52z     Sep 2002 78910 Posts P-1 found a factor in stage #2, B1=530000, B2=9805000. UID: Jwb52z/Clay, M58188989 has a factor: 55849484816777970918764473 85.530 bits.
 2012-10-11, 16:45 #555 harlee     Sep 2006 Odenton, MD, USA 22·41 Posts Two factors found with Brent-Suyama: P-1 found a factor in stage #2, B1=260000, B2=6305000, E=12. M4037023 has a factor: 46132411290706485444839 k = 5713667136737453 = 17 × 31 × 53 × 1327 × 154,154,969 P-1 found a factor in stage #2, B1=290000, B2=7395000, E=12. M4438789 has a factor: 1402524780745530895151 k = 157985069885675 = 5^2 × 73883 × 85,532,569
 2012-10-13, 09:41 #556 aketilander     "Åke Tilander" Apr 2011 Sandviken, Sweden 56610 Posts A big one ANONYMOUS Manual testing 1019 F-ECM Oct 13 2012 2:05AM 0.0 0.0000 1140356877758679056056869944845540826402854641895928218298013381554156431441 249.334 bits Quote from http://www.mersenne.org/report_recent_cleared/ There are now 4 known factors of M1019 with a total size of 452.3 bits Factor was not found by me. It would be interesting to know who was the "Anonymous" this time? 13th biggest known factor of any Mp (not counting the biggest factors of fully factored Mps). Does anyone know wether the remaining 567-bit factor is composite or not? OK Now I have found this post. Adding a question: Does "prp" in frmky:s log mean that the factors are probable primes, not proven to be primes? Last fiddled with by aketilander on 2012-10-13 at 10:39
 2012-10-13, 10:16 #557 Jatheski     Apr 2012 993438: i1090 2·73 Posts Found by NFS@home http://escatter11.fullerton.edu/nfs/...ead.php?id=386 The remaining 567-bit factor is prime Last fiddled with by Jatheski on 2012-10-13 at 10:16
2012-10-13, 17:34   #558
Dubslow

"Bunslow the Bold"
Jun 2011
40<A<43 -89<O<-88

1C3516 Posts

Quote:
 Originally Posted by aketilander Adding a question: Does "prp" in frmky:s log mean that the factors are probable primes, not proven to be primes?
Techinically, yes, but with numbers > 30-50 digits, the chance of prp-liar is incredibly small, small enough that no one usually bothers to check it. Besides, the FactorDB automatically checks primality of all numbers < 300 digits (and there are many programs/methods to do larger numbers).

2012-10-13, 18:13   #559
aketilander

"Åke Tilander"
Apr 2011
Sandviken, Sweden

2×283 Posts

Quote:
 Originally Posted by Dubslow Techinically, yes, but with numbers > 30-50 digits, the chance of prp-liar is incredibly small, small enough that no one usually bothers to check it. Besides, the FactorDB automatically checks primality of all numbers < 300 digits (and there are many programs/methods to do larger numbers).
Thanks Dubslow, I keep forgetting about FactorDB, its so useful!

2012-10-14, 08:37   #560
gd_barnes

May 2007
Kansas; USA

2×3×11×157 Posts

Quote:
 Originally Posted by TObject ECM found a factor in curve #1, stage #0 Sigma=4307542445565784, B1=50000, B2=250000. M268435456 has a factor: 85 What did I win? LOL
Quote:
 Originally Posted by ET_ A math book on Mersenne factors? 85 has not the form 2kp+1... and 268435456 is 228 and not prime. Luigi
M268435456 does have a factor of 85. Although 85 and 268435456 happen to be composite, it does not invalidate the statement made, even if such statement is not mathematically relevant here.

For what it's worth:

M268435456 = 3 * 5 * 17 * 257 * 641 * 65537 * 6700417 * ??

Or more interestingly M(2^28) = (2^1+1) * (2^2+1) * (2^4+1) * (2^8+1) * (2^16+1) * (2^32+1) * ??
Note that 2^32+1 = 641 * 6700417.

Edit:
The question is: How long does this sequence continue? In other words are 2^64+1 and 2^128+1 factors also?

Last fiddled with by gd_barnes on 2012-10-14 at 09:36 Reason: edit

 2012-10-15, 00:16 #561 gd_barnes     May 2007 Kansas; USA 101000011110102 Posts After some analysis, I just answered my own question above. I'm sure many on here recognize this but I did not. I'll state it for others like me who did not know the following: For any 2^(2^q)-1 where q is sufficiently large, algebraic factors are: Code: [2^(2^0)+1] * [2^(2^1)+1] * [2^(2^2)+1] * [2^(2^3)+1] * [2^(2^4)+1] * ..... * [2^(2^(q-1))+1] Therefore M268435456, which represents 2^(2^28)-1 = Code: [2^(2^0)+1] * [2^(2^1)+1] * [2^(2^2)+1] * [2^(2^3)+1] * [2^(2^4)+1] * ..... * [2^(2^27)+1] Obviously these are not all prime factors but it is a good starting point for full prime factorization. Last fiddled with by gd_barnes on 2012-10-15 at 00:21

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