Home Primes, Reloaded

[paleseptember]

is prime. Was trying (not-so) random starting points :D

[mdettweiler]

I've advanced 6138 a bit, to i=52, size 93, C93.

[richs]

8960 to i54, size 104, C101

[kar_bon]

Originally Posted by mdettweiler

I've advanced 6138 a bit, to i=52, size 93, C93.

recommended to all users:

i saw the index 52 was a pure C93, so i tested it with the QuickECM-option of the FactoringDatabase.

the first run turns it in P6*C87

the second run splitted the C87 into P20*P67!

so please, try the great QuickECM-option before giving up!

now it's at index 56 with a C96 (no more factors with QuickECM > next factor should be greater 30 digits)

[gd_barnes]

It's interesting that you mention that Karsten. ~80% of the work that I did above was solely with quick ECM. I had to use msieve to initially break a majority of the C62-C75 but after that, quick ECM usually took it up many indexes with only a couple of msieve runs thrown in.

Hint to all: I always do quick ECM at least 5 times on each # before giving up or using msieve. Many times it will factor on the 3rd/4th/5th try. I can even remember one day I had my 2 cores that I usually run msieve on running on something else and I didn't want to slow it down by running a 3rd program on the machine. So I tried doing quick ECM on a C69 something like 10-15 times and wouldn't you know...it factored on the final try. I remember I was going to give up after 2 more attempts.

Quick ECM is a great tool but it is a little quirky. Don't give up after trying it once or twice. I suspect there is some sort of built in curve randomizer so that it tries different curves each time you hit it. So you may try it 10 times with no luck but alas, it will factor it for you on the 11th try.

BTW, in response to your final sentence about the next factor "should" be at least 30 digits. That's not necessarily true. I've hit quick ECM 10 times and it still didn't end up finding what turned out to be a P28 or P29. On the other hand, I've had it find a P34 or P35 on the first try. Like I said, it can be a little quirky. Several weeks ago, I remember it even had a hard time factoring some C21s thru C23s. I saw the issue brought up in another thread and apparently it got fixed.


Gary

[kar_bon]

the 30 digits is only my observation. i got a P28 or P29 left, too. or QuickECM found some P32 as well.

instead of msieve i use yafu (version 1.12 with an ini-file and 4 threads on my Quad) because it's way faster for upto 90 digits. because yafu don't use 100% processtime when running (i think because of saving the relations found) other programs will continue their work (at about 5-10% CPU-use) although yafu can end the job quite quick!
so no need to shut down other programs and start yafu.
the HomePrimes are growing fast in digits so there is not much work to do manually.

at lower index i need 3 (sometimes 4 when a number is not fully factored) mouse-clicks for an index:
- open a seq in a new window: the last unfactored part will be shown below "Sequence ended: not all factors known"
a) click (1) on the factor
b) click (2) "Quick ECM" -> factors shown
c) click (3) on the seq-number below "Additional info"

begin at a) again.
at higher index you habe to click more as mentioned.

it's the easiest way until there's no special program like aliqueit

[gd_barnes]

That's exactly the way I've been advancing many of the sequences, sometimes 10 indexes or more starting from a C70. I'll have to try yafu instead.

In the mean time, I tried a different way of looking at your page. I decided to attempt to factor using only fast ECM (or msieve on C<=75 that would not fast ECM) on all of the sequences where there was either a 0 or 1 digit difference between the size and the remaining factor. Kind of like what you did with Max's sequence when you saw there was no difference. I figured those had a better chance than normal of not having the fast ECM previously used. There were probably about 30-35 of them and I was able to advance 12 sequences. A few were only advanced 2-3 indexes but several were able to be advanced by 5-10 indexes. I was disappointed not to find any primes. Here they are:

2138, i=59, sz 106, C98
2147, i=64, sz 104, C95
2618, i=46, sz 95, C85
3192, i=51, sz 92, C79
3215, i=54, sz 102, C101*
3867, i=53, sz 99, C97
5368, i=56, sz 103, C93
5632, i=44, sz 93, C88
7210, i=59, sz 111, C82
7554, i=51, sz 100, C97
8729, i=47, sz 87, C86*
9529, i=54, sz 88, C81

* - Advanced from a difference of 1 that easily factored to a different difference of 1 that would not easily factor.

There are a TON of C71's and C72's in the DB. (I got rid of all C<=70.) I would guess that 20-30% of those will fast ECM. If not, then a quick msieve/yafu to factor them followed by fast ECM to advance them several more indexes will be quite effective. I think we're still a long way away from not being able to easily use fast ECM for home prime base 10 sequences <= 10200.


Gary

[gd_barnes]

I found two C<70 that popped up in the DB so I had to get rid of them. One worked its way to a prime! Here they are:

7343, i=44, sz 78, prime
7615, i=51, sz 95, C85

[mataje]

I am doing C<80 using Quick ECM and Yafu. N<4500 done.

[RichD]

At first I was randomly picking a few HP(10)s to factor. Then I started following this thread so I won't step on other's toes. I began around c74's. Maybe doing a c73 & c75 here or there. It was so easy at first I popped 5-6 the first night. Didn't think it was worth reporting. Then it slowed down. Last night will be my last night for about 5 days before I can do anymore. I probably did 10-12 but I have no record of which ones.

Going forward I may try to keep a list of mine.

RichD.

[richs]

9937 to i58, size 122, C114