mersenneforum.org Sieving freakishly big MMs (was "World record" phone number?)
 Register FAQ Search Today's Posts Mark Forums Read

 2012-09-26, 09:22 #34 ET_ Banned     "Luigi" Aug 2002 Team Italia 3·1,619 Posts So, AFAICT, MM43112609 has been "trial-factored" up to k=4, right? What about MM42643801 and MM32582657? MM30402457 and MM25964951 Are at k=40 and k=44 respectively (thanks to Phil Moore). Luigi
2012-09-26, 09:26   #35
axn

Jun 2003

2×2,719 Posts

Quote:
 Originally Posted by Batalov Don't die laughing. Promise? Ok. 15*2^43112611-59 completed P-1, B1=150000, B2=3000000, We4: 5B5B93C9
ha!
Code:
185*2^43112610-369 completed P-1, B1=10000, B2=300000, We1: 5B6E3988
201*2^43112610-401 completed P-1, B1=10000, B2=300000, We1: 5B6E3988
so there! (note the one fewer zero?)

2012-09-26, 09:29   #36
axn

Jun 2003

543810 Posts

Quote:
 Originally Posted by ET_ So, AFAICT, MM43112609 has been "trial-factored" up to k=4, right?
Nope. As per LaurV's pre-screening, k=185 is the smallest viable candidate. So k=184.

 2012-09-26, 09:34 #37 ET_ Banned     "Luigi" Aug 2002 Team Italia 113718 Posts Code: 201*2^43112610-401 completed P-1, B1=10000, B2=300000, We1: 5B6E3988 That would mean no factors less than 300,000 for k=201 in 2*201*2^43112610-1 ... correct? Luigi
2012-09-26, 09:40   #38
ET_
Banned

"Luigi"
Aug 2002
Team Italia

113718 Posts

Quote:
 Originally Posted by axn Nope. As per LaurV's pre-screening, k=185 is the smallest viable candidate. So k=184.
Code:
M( M( 32582657 ) )U: k=0                #
M( M( 42643801 ) )U: k=0                #
M( M( 43112609 ) )U: k=184              # LaurV, pre-screening, 2012 Sep 26
Waiting for the other 2...

Luigi

2012-09-26, 11:22   #39
axn

Jun 2003

2·2,719 Posts

Quote:
 Originally Posted by ET_ That would mean no factors less than 300,000 for k=201 in 2*201*2^43112610-1 ... correct?
Not quite. This is P-1 bounds, so it is hard to translate it into a TF bound. However, LaurV, I believe, has TF'ed it to 10G.

Quote:
 Originally Posted by ET_ Code: M( M( 32582657 ) )U: k=0 # M( M( 42643801 ) )U: k=0 # M( M( 43112609 ) )U: k=184 # LaurV, pre-screening, 2012 Sep 26 Waiting for the other 2... Luigi
Ok. After sieving to 3G, 42643801's lowest viable candidates are k={33,69,96}. So you can call it covered till k=32. I am doing 32582657 now.

 2012-09-26, 11:40 #40 axn     Jun 2003 2×2,719 Posts After sieving to 4G, 32582657's lowest viable candidates are k={20,60,108}. So you can call it covered till k=19.
2012-09-26, 12:14   #41
axn

Jun 2003

2×2,719 Posts

Quote:
 Originally Posted by LaurV For k being 0 or 1 (mod 4) type (the "can be a factor of MMp" type), we have k=185, 201 (both tested to 10G) and 233 (2G55), 273 (2G),384 (2G55), and 513, 521, 560, 593, 656 (all tested to 1G) and few more which I don't remember right now. All k under 1000, for this k type, were tested to 1G.
A quick sieve to 4G gives the following survivors under 1000
Code:
185
201
233
273
384
513
521
560
593
656
660
665
668
684
713
753
800
809
860
888
944
965
Quote:
 Originally Posted by LaurV Sure, what I wanted to say was "testing them higher by this method of trial factoring will not prove their primality". After I read your post I see that it could be interpreted as "it is impossible to prove them prime by any method".
Gotcha.

 2012-09-26, 18:36 #42 ewmayer ∂2ω=0     Sep 2002 República de California 5×2,351 Posts Nice work on the sieve, guys - this matches my own factor.c sieve results for the smaller-primes prescreening. For q's passing the small-prime sieve we definitely want to sieve very deeply (by the standards of such sieves - even 2^64 is tiny relative to q here), in order to, say, double the odds of q being prime from {very tiny) to 2*(very tiny). As has been noted elsewhere, once we've sieved/p-1'd/ecm'ed q as deeply as we reasonably can, there is little point in attempting a direct nonfactorial compositeness test, since it is cheaper at that point to simply check whether q divides MMp. If q is composite it has no chance of dividing MMp; if q is prime it has at least a modest chance.
2012-09-27, 08:35   #43
ET_
Banned

"Luigi"
Aug 2002
Team Italia

3×1,619 Posts

Quote:
 Originally Posted by ewmayer Nice work on the sieve, guys - this matches my own factor.c sieve results for the smaller-primes prescreening. For q's passing the small-prime sieve we definitely want to sieve very deeply (by the standards of such sieves - even 2^64 is tiny relative to q here), in order to, say, double the odds of q being prime from {very tiny) to 2*(very tiny). As has been noted elsewhere, once we've sieved/p-1'd/ecm'ed q as deeply as we reasonably can, there is little point in attempting a direct nonfactorial compositeness test, since it is cheaper at that point to simply check whether q divides MMp. If q is composite it has no chance of dividing MMp; if q is prime it has at least a modest chance.
Hi Ernst, the last 4 DM have been sieved up to 7G.

Should we proceed with PARI up to a defined level, or you may show us a better sieving method?

Luigi

2012-09-27, 18:36   #44
gd_barnes

"Gary"
May 2007
Overland Park, KS

2E4516 Posts

Quote:
 Originally Posted by ewmayer As has been noted elsewhere, once we've sieved/p-1'd/ecm'ed q as deeply as we reasonably can, there is little point in attempting a direct nonfactorial compositeness test, since it is cheaper at that point to simply check whether q divides MMp. If q is composite it has no chance of dividing MMp; if q is prime it has at least a modest chance.
That all depends on whether you want to find a world record prime of the form 2*k*M43112609+1 or find a factor of MM43112609. It would be very cool to find a world record prime that is not a Mersenne; not that that is likely to happen anytime soon.

 Similar Threads Thread Thread Starter Forum Replies Last Post CRGreathouse Number Theory Discussion Group 51 2018-12-16 21:55 LaurV Hobbies 74 2018-07-11 19:33 Batalov Computer Science & Computational Number Theory 40 2013-03-16 09:19 outlnder Soap Box 20 2005-02-03 09:30 nitai1999 Software 7 2004-08-26 18:12

All times are UTC. The time now is 02:13.

Mon Feb 6 02:13:45 UTC 2023 up 171 days, 23:42, 1 user, load averages: 1.26, 1.17, 1.10