Tony Forbes writes:
I know it's a bit feeble the usual standards for ECM factorization, but
Seems to me that "feeble" certainly doesn't include factors that are
new! Besides, I'm doing some work on 11-digit factors.:)
I just found this 36-digit factor of 2^2203+1 :
848425589476255002200418022118728331
Great!
Thus 2^2203+1 = 3 * 13219 * 208613913329 * 743372438374143806443 *
282324958084937237369 * 848425589476255002200418022118728331 * C571
I apologise if this is not new or not interesting.
New factors are always interesting, at least to me. And "new" is
relative; I don't always have time to update my web pages each week.
I am still trying to find numbers n > 1000 where gcd(n, 30) = 1 and 2^n-
1 and 2^n+1 are completely factorized. Like 2203 would be once the C571
part has been factorized (2^2203-1 is prime). The only ones I know are
1121 and 1141. Anyone know of any more?
There may be more in my data; check:
http://www.garlic.com/~wedgingt/factoredM.txt
Note that 2^n - 1 is listed there with n as the exponent; 2^n + 1
is listed there with 2*n as the exponent, since:
2^(2*n) - 1 = (2^n - 1)*(2^n + 1)
by the difference of squares factoring method. E.g., take the case of
2^2203 + 1; it's listed under 'M( 4406 )' but does not include the
first factor listed above (3) since that is also a factor of a smaller
Mersenne number (M(2)). (If this wasn't done, 3 would be listed next
to all even exponents, 7 next to all exponents that are multiples of
3, 5 next to all that are multiples of 4, etc; see ecm3.c of the mers
package for how this is done).
Will
P.S. Here's the most recent run of a new program of mine:
+ 1strs8gmp -r617 32768 13000000069 13100000000
M( 20163 )C: 13001425009
M( 24603 )C: 13013067967
M( 28795 )C: 13014015431
M( 30644 )C: 13015272901
M( 19130 )C: 13016377211
M( 16105 )C: 13032166001
M( 10997 )C: 13032852617
M( 13762 )C: 13034540681
M( 20190 )C: 13044597481
M( 11660 )C: 13051970801
M( 17388 )C: 13053675853
M( 5358 )C: 13062782569
M( 7160 )C: 13070164721
M( 13414 )C: 13078100027
M( 13428 )C: 13098436597
M( 7292 )C: 13098758149
It printed all factors (from 13 to 13.1 billion) that are not already
in my data of all Mersenne numbers between the two arguments to -r
(617 and 2^15, here). It took about 6 hours this morning on my new
P233MMX CPU (my P200's mainboard appears to have fried Sunday night in
a power outage & surge; sorry if email to me bounced in the mean time.
I believe that no data was lost, though I still have some bad blocks
to fix/redirect).
Note that it would run at the same speed if the limit on the exponent
were removed, but it would be full of data for composite exponents up
to the size of the factor.
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