largest factor ,i think.

heryu · 2004-09-03, 10:15

i found a largest factor of M65536 i think ,what to do next.
please help me,thanks.

ET_ · 2004-09-03, 11:30

Quote:

Originally Posted by heryu

i found a largest factor of M65536 i think ,what to do next.
please help me,thanks.

M65536 is not a true Mersenne number, as 65536 is not prime...

BTW, what program did you use, and which factor did you find?

Luigi

R.D. Silverman · 2004-09-03, 11:43

Quote:

Originally Posted by heryu

i found a largest factor of M65536 i think ,what to do next.
please help me,thanks.

Not only is 65536 not prime, but M65536 splits into a LOT of algebraic
factors

M65536 = M32768 * P32768 = M16384 * P16384 * P32768 =
M8192 * P8192 * P16384 * P32768 = ... etc. etc.....

Now If you are claiming a new factor of F15 or F14 etc., that would be
noteworthy!

wblipp · 2004-09-03, 12:02

Quote:

Originally Posted by heryu

i found a largest factor of M65536 i think ,what to do next.
please help me,thanks.

First you should determine if this is really a new factor. Will Edgington is the world's keeper of Mersenne Factors. He regularly updates lists of all known factors for exponents up to 200,000 on Will Edgington's Mersenne Page. The most recent update was yesterday.

To read Will's files you need to understand about algebraic factors. In your case this is simple. 2⁶⁵⁵³⁶-1 factors into

(2³²⁷⁶⁸+1)
(2¹⁶³⁸⁴+1)
(2⁸¹⁹²+1)
(2⁴⁰⁹⁶+1)
etc.

Note that Will lists the factors of (2^k+1) under M(2k).

Some of the known factors are:

M( 65536 )C: 4659775785220018543264560743076778192897
M( 65536 )C: 7455602825647884208337395736200454918783366342657
M( 16384 )C: 319546020820551643220672513
M( 8192 )C: 1256132134125569

When your number is less the 10,000 digits, you can use

Dario Alpern's Java Applet to look up the known factors. Dario regularly gets the latest factor files from Will Edgington and Richard Brent. While your number is too large, the two "top level" factors of (2³²⁷⁶⁸+1) and (2³²⁷⁶⁸-1) fit.

If your factor is new, then send Will Edgington an email and it will appear in the next release of his files. Then brag a little bit. Here and the Yahoo PrimeNumbers list are good places to brag.

William

heryu · 2004-09-04, 10:12

it is 148 digits .

ET_ · 2004-09-04, 18:51

Quote:

Originally Posted by heryu

it is 148 digits .

384 bits?

Luigi

geoff · 2004-09-04, 23:25

Quote:

Originally Posted by heryu

it is 148 digits .

The largest known prime factor of M65536 is 49 digits, and the largest ever found by ECM for any number is 58 digits I think, so yours is almost certainly a composite, possibly of already known factors.

If so and you found it with Prime95 then make sure you have a copy of http://www.mersenne.org/gimps/lowm.txt in Prime95's working directory to avoid finding already known factors in the future.

(If not, then congratulations!)

wblipp · 2004-09-05, 05:11

Quote:

Originally Posted by geoff

The largest known prime factor of M65536 is 49 digits, and the largest ever found by ECM for any number is 58 digits I think, so yours is almost certainly a composite, possibly of already known factors.

Use Dario Alpern's Web Applet to see if the number is prime:

http://www.alpertron.com.ar/ECM.HTM

geoff · 2004-09-06, 01:49

Quote:

Originally Posted by geoff

The largest known prime factor of M65536 is 49 digits

That is wrong, there are larger known prime factors, it seems 49 digits is just the largest one listed in lowm.txt which I guess means it is the largest one found by ECM or similar methods.

philmoore · 2004-09-07, 20:12

Does your 148-digit factor end in a 5? If so, you have found a 148-digit composite which is probably a product of known factors of Fermat numbers. Factor your number using Dario Alpern's factoring applet and then check the factors listed at:
http://www.prothsearch.net/fermat.html
If you found this factor using Prime95, download lowm.txt first.

heryu · 2004-09-08, 11:15

Quote:

Originally Posted by philmoore

Does your 148-digit factor end in a 5? If so, you have found a 148-digit composite which is probably a product of known factors of Fermat numbers. Factor your number using Dario Alpern's factoring applet and then check the factors listed at:
http://www.prothsearch.net/fermat.html
If you found this factor using Prime95, download lowm.txt first.

yeah it is end in a 5,
thanks for you all .

2004-09-03, 10:15	#1
heryu Jun 2004 2² Posts	largest factor ,i think. i found a largest factor of M65536 i think ,what to do next. please help me,thanks.

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2004-09-04, 10:12	#5
heryu Jun 2004 2² Posts	it is 148 digits .

2004-09-07, 20:12	#10
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2⁵·5·7 Posts	Does your 148-digit factor end in a 5? If so, you have found a 148-digit composite which is probably a product of known factors of Fermat numbers. Factor your number using Dario Alpern's factoring applet and then check the factors listed at: http://www.prothsearch.net/fermat.html If you found this factor using Prime95, download lowm.txt first.