[QUOTE=ET_;313696]A math book on Mersenne factors? :smile:

85 has not the form 2kp+1...
and 268435456 is 2[sup]28[/sup] and not prime.

Luigi[/QUOTE]

Did whoever created the [url=http://www.mersenne.org/report_ECM/]ECM Progress[/url] report on PrimeNet also win the said book? LOL

Composite exponent + composite divisor= ?

[QUOTE=TObject;313740]Did whoever created the [url=http://www.mersenne.org/report_ECM/]ECM Progress[/url] report on PrimeNet also win the said book? LOL[/QUOTE]

[QUOTE=FTFP][B][SIZE="7"]ECM on Fermat numbers[/SIZE][/B][/QUOTE]

Fermat number = 2^xxxx[B][COLOR="Red"]+[/COLOR][/B]1

P-1 found a factor in stage #2, B1=530000, B2=9805000.
UID: Jwb52z/Clay, M58188989 has a factor: 55849484816777970918764473

85.530 bits.

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

A big one
 

ANONYMOUS Manual testing 1019 F-ECM Oct 13 2012 2:05AM 0.0 0.0000 1140356877758679056056869944845540826402854641895928218298013381554156431441

249.334 bits

Quote from [URL]http://www.mersenne.org/report_recent_cleared/[/URL]

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?

[URL="http://www.mersenne.org/report_factors/?exp_lo=1&exp_hi=100000&exp_date=&fac_len=76&dispdate=1&B1=Get+Factors"]13th biggest known factor of any Mp[/URL] (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 [URL="http://www.mersenneforum.org/showpost.php?p=314446&postcount=175"]this post[/URL].

Adding a question: Does "prp" in frmky:s log mean that the factors are probable primes, not proven to be primes?

Found by NFS@home
[URL]http://escatter11.fullerton.edu/nfs/forum_thread.php?id=386[/URL]

The remaining 567-bit factor is prime

[QUOTE=aketilander;314481]
Adding a question: Does "prp" in frmky:s log mean that the factors are probable primes, not proven to be primes?[/QUOTE]

Techinically, yes, but with numbers > 30-50 digits, the chance of prp-liar is [i]incredibly[/i] small, small enough that no one usually bothers to check it. Besides, the [URL="http://factordb.com/index.php?query=M1019"]FactorDB[/URL] [URL="http://factordb.com/index.php?id=1100000000543628119"]automatically[/URL] [URL="http://factordb.com/index.php?id=1100000000543628120"]checks[/URL] primality of all numbers < 300 digits (and there are many programs/methods to do larger numbers).

[QUOTE=Dubslow;314524]Techinically, yes, but with numbers > 30-50 digits, the chance of prp-liar is [I]incredibly[/I] small, small enough that no one usually bothers to check it. Besides, the [URL="http://factordb.com/index.php?query=M1019"]FactorDB[/URL] [URL="http://factordb.com/index.php?id=1100000000543628119"]automatically[/URL] [URL="http://factordb.com/index.php?id=1100000000543628120"]checks[/URL] primality of all numbers < 300 digits (and there are many programs/methods to do larger numbers).[/QUOTE]

Thanks Dubslow, I keep forgetting about FactorDB, its so useful!

[QUOTE=TObject;313675]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]

[QUOTE=ET_;313696]A math book on Mersenne factors? :smile:

85 has not the form 2kp+1...
and 268435456 is 2[sup]28[/sup] and not prime.

Luigi[/QUOTE]

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?

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]
[/code]

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]
[/code]

Obviously these are not all prime factors but it is a good starting point for full prime factorization.