Sieving freakishly big MMs (was "World record" phone number?) - Page 4

ET_ · 2012-09-26, 09:22

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

axn · 2012-09-26, 09:26

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?)

axn · 2012-09-26, 09:29

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.

ET_ · 2012-09-26, 09:34

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

ET_ · 2012-09-26, 09:40

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

axn · 2012-09-26, 11:22

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.

axn · 2012-09-26, 11:40

After sieving to 4G, 32582657's lowest viable candidates are k={20,60,108}. So you can call it covered till k=19.

axn · 2012-09-26, 12:14

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:

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.

ewmayer · 2012-09-26, 18:36

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.

ET_ · 2012-09-27, 08:35

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

gd_barnes · 2012-09-27, 18:36

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.

2012-09-26, 09:34	#37
ET_ Banned "Luigi" Aug 2002 Team Italia 3·1,619 Posts	Code: 2012^43112610-401 completed P-1, B1=10000, B2=300000, We1: 5B6E3988 That would mean no factors less than 300,000 for k=201 in 2201*2^43112610-1 ... correct? Luigi

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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, 11:40	#40
axn Jun 2003 5436₁₀ 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, 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.