fond of a factor? Urn yourself to become remains

[TObject]

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

[c10ck3r]

Composite exponent + composite divisor= ?

[axn]

Originally Posted by TObject

Did whoever created the ECM Progress report on PrimeNet also win the said book? LOL

Originally Posted by FTFP

ECM on Fermat numbers

Fermat number = 2^xxxx+1

[Jwb52z]

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

85.530 bits.

[harlee]

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

[aketilander]

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?

[Jatheski]

Found by NFS@home
http://escatter11.fullerton.edu/nfs/...ead.php?id=386

The remaining 567-bit factor is prime

[Dubslow]

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).

[aketilander]

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!

[gd_barnes]

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

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?

[gd_barnes]

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:

[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 =

[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.