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2017-10-06, 09:12   #1
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

18F016 Posts
3-brilliant

Code:
10^85 + 107473 =
12347174190853644923628605843 *
18988823498425240613108727011 *
42651505675667342634613401401
The attached file contains, for every n<=107473 with (10^85+n,10^6!)==1, either the word 'PRIME' if 10^85+n is prime, or a prime factor. For the numbers where the displayed factor is not of 29 digits, that's evidence; for the 29-digit numbers it should be straightforward to check that the cofactor is prime.

I think this is new; at least it's not on

https://www.alpertron.com.ar/BRILLIANT3.HTM#min3br

This is an exercise in data management and figuring out good points to switch ECM levels; took about two CPU-weeks which were mostly spent in the final msieve jobs to finish the gaps; the data management is helped by noticing that you can recover n from p (as p-lift(Mod(10,p)^85) so don't need to maintain the matching except when compiling the final table.

I am most of the way through doing the same thing for 10^88+n
Attached Files
 certificate.gz (44.3 KB, 95 views)

Last fiddled with by fivemack on 2017-10-06 at 09:20

 2017-10-09, 15:46 #2 chris2be8     Sep 2009 32×227 Posts Factoring (4762271^19-1)/2999339555510 produced: Code: p39 factor: 104426665673144738814918007495550408497 p39 factor: 131594475136416936581040193488397035331 p39 factor: 183397454399731007619541358534329559279 I'd have posted it in the Gratuitous Factors thread if this one hadn't been started. Chris
2017-10-11, 08:58   #3
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

24·3·7·19 Posts

10^85 - 224621 =
Code:
16590231029548214398579319783 *
21620099167674771100153066907 *
27879814796486104536348179759
Certificate attached, which works in the same way as for 85+
Attached Files
 certificate-85m.gz (92.5 KB, 102 views)

2017-10-11, 20:09   #4
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

11000111100002 Posts

10^88 - 697107 =
Code:
112582261378919338123979183167 *
120894766377814164001721854681 *
734721133070772150681018962059
This is the largest 88-digit number which splits as a product of three thirty-digit primes; certificate attached.
Attached Files
 certificate-88M.gz (256.6 KB, 96 views)

2017-11-02, 22:36   #5
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

638410 Posts

Code:
10^100 - 3302127 =
1081699593131182743410694185335271 *
2147178415105826474267811749381803 *
4305515935360678535609171490104021
Certificate attached in the same form as previously.

I'd send this to alpertron, but I haven't heard back about the previous ones I've sent there.

One oddity when doing this: 10^50 + 1623 and 10^50 - 1623 are both prime, so 10^100-2634129 survived lots of ECM, and failed (sieving giving a yield of zero) when I tried SNFS with the reducible polynomial x^4-1623^2.
Attached Files
 certificate.100M.gz (1.13 MB, 91 views)

Last fiddled with by fivemack on 2017-11-02 at 22:40

 Similar Threads Thread Thread Starter Forum Replies Last Post alpertron Factoring 50 2013-05-27 11:21 fivemack Miscellaneous Math 13 2012-05-03 23:56 Citrix Prime Sierpinski Project 12 2006-05-19 22:21

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