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Old 2012-09-26, 09:22   #34
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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
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Old 2012-09-26, 09:26   #35
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Quote:
Originally Posted by Batalov View Post
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?)
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Old 2012-09-26, 09:29   #36
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Quote:
Originally Posted by ET_ View Post
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.
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Old 2012-09-26, 09:34   #37
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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?

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Old 2012-09-26, 09:40   #38
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Quote:
Originally Posted by axn View Post
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...

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Old 2012-09-26, 11:22   #39
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Quote:
Originally Posted by ET_ View Post
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_ View Post
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.
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Old 2012-09-26, 11:40   #40
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After sieving to 4G, 32582657's lowest viable candidates are k={20,60,108}. So you can call it covered till k=19.
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Old 2012-09-26, 12:14   #41
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Quote:
Originally Posted by LaurV View Post
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 View Post
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.
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Old 2012-09-26, 18:36   #42
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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.
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Old 2012-09-27, 08:35   #43
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Quote:
Originally Posted by ewmayer View Post
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
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Old 2012-09-27, 18:36   #44
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Quote:
Originally Posted by ewmayer View Post
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.
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