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-   -   Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

EdH 2022-04-06 11:47

[QUOTE=garambois;603367]Excellent !
As far as I know, the record is held by you with the calculation of 2^549 which ends on a P165 ![/QUOTE]Thanks! Might be difficult to break that one for a while, but maybe with some of the larger ones I'm trying to bring down.

charybdis 2022-04-06 12:50

Surely the record is held by 2^82589933? :razz:

EdH 2022-04-06 13:08

[QUOTE=charybdis;603391]Surely the record is held by 2^82589933? :razz:[/QUOTE]Point taken.

garambois 2022-04-06 14:34

[QUOTE=charybdis;603391]Surely the record is held by 2^82589933? :razz:[/QUOTE]
You are right, but the difference is precisely that we know the prime of the end for the sequence 2^549, which is not the case for 2^82589933 !

EdH 2022-04-06 14:42

[QUOTE=garambois;603402]You are right, but the difference is precisely that we know the prime of the end for the sequence 2^549, which is not the case for 2^82589933 ![/QUOTE]Isn't it 2^82589933-1?

garambois 2022-04-06 15:14

[QUOTE=EdH;603404]Isn't it 2^82589933-1?[/QUOTE]

Oh, yes, you're right, I got it all wrong on that one.
It's a Mersenne prime number, I didn't pay attention.
But FactorDB remained silent on this when I submitted this request !

EdH 2022-04-06 17:33

[QUOTE=garambois;603405]Oh, yes, you're right, I got it all wrong on that one.
It's a Mersenne prime number, I didn't pay attention.
But FactorDB remained silent on this when I submitted this request ![/QUOTE]I think that's because factordb doesn't recognize Mersenne numbers as such and would need to perform the expression, factor all the 2s and then perform the sigma function. It's probably past some limit.

RichD 2022-04-06 22:57

Base 103 can be added at the next update.
A few short terminating runs are available for this base.

EdH 2022-04-07 03:22

[QUOTE=RichD;603434]Base 103 can be added at the next update.
A few short terminating runs are available for this base.[/QUOTE]Thanks Rich. My scripts run off the tables, so I'll add the short runs to the other thread after the table is added.

garambois 2022-04-12 14:58

Page updated.
Many thanks to all for your help.

[B]Added bases : 80, 103.[/B]
[B]Several bases have been updated according to your indications and the progress of my own calculations.[/B]

@firejuggler :
I don't know if all the recently completed sequences for base 660 should be attributed to you ?
Unless I am mistaken, you have only claimed the calculation of the 660^50 sequence.
Are the attributions for base 660 correct ?

@birtwistlecaleb :
Does the acronym "BIR" suit you ?

EdH 2022-04-12 16:00

In the base 101 table, you've got BRI instead of BIR for ^53 and ^77. Perhaps that's just while awaiting confirmation. . .:smile:

I believe you added 101 last time ([URL="https://www.mersenneforum.org/showpost.php?p=602686&postcount=1543"]#1543[/URL]) and now have added 103. Is that correct?

Sorry to be such a pain.:smile:

Thanks for all your work!

garambois 2022-04-12 19:02

But what was I thinking today ?
Thank you Edwin for all these error reports, what a perceptive eye !

I'm waiting for the confirmation for the "BIR" acronym and I'll correct it.

Yes, it was indeed base 103 !
If you want, you can correct my post #1562.

Many thanks to you too Edwin for all your help !

EdH 2022-04-12 19:37

[QUOTE=garambois;603842]. . .
Yes, it was indeed base 103 !
If you want, you can correct my post #1562.
. . .[/QUOTE]I did.

I'm seeing a few terminations that haven't been updated. Do your scripts check all bases or do you have to tell them which ones to check. Perhaps those bases were run before the sequences terminated?
Examples:[code]3^323: Prime \
3^329: Prime - All matched parity sequences in this table now terminated!
3^331: Prime /
5^219: Prime
5^221: Prime
5^223: Prime
6^202: Prime
18^134: Prime
28^88: Prime
30^100: Prime - All matched parity sequences in this table now terminated!
37^99: Prime - All matched parity sequences in this table now terminated!
45^87: Prime
48^86: Prime
51^83: Prime
82^72: Prime
90^72: Prime[/code]I'll quit pestering you now and go back to my play for a while.:smile:

garambois 2022-04-13 07:46

[QUOTE=EdH;603844]I did.
[/QUOTE]
A lot of thanks !


[QUOTE=EdH;603844]
I'm seeing a few terminations that haven't been updated. Do your scripts check all bases or do you have to tell them which ones to check. Perhaps those bases were run before the sequences terminated?
[/QUOTE]
No, the scripts cannot scan all the databases at once because of the restrictions put in place on FactorDB.
[B]I would like to take this opportunity to appeal again to the FactorDB administrators: It's a real pain to work with these new restrictions ![/B]


[QUOTE=EdH;603844]
Examples:[code]3^323: Prime \
3^329: Prime - All matched parity sequences in this table now terminated!
3^331: Prime /
5^219: Prime
5^221: Prime
5^223: Prime
6^202: Prime
18^134: Prime
28^88: Prime
30^100: Prime - All matched parity sequences in this table now terminated!
37^99: Prime - All matched parity sequences in this table now terminated!
45^87: Prime
48^86: Prime
51^83: Prime
82^72: Prime
90^72: Prime[/code][/QUOTE]
There must be something I didn't understand !
When I do an update, because of the restrictions put in place on FactorDB, I only scan the bases for which I have been notified of sequences that have terminated.
These notifications are done on [URL="https://www.mersenneforum.org/showthread.php?t=27659"]this thread[/URL].
Now, unless I am mistaken, nowhere on the thread can I find a report that for example 3^323, 3^329, 3^331 end.
As a result, I have no idea to whom I should attribute all these calculations reported above ?
Forgive me if I missed something obvious on the thread !

I don't know how to make sure I don't miss any completed sequences and associate the right attribution to them if they are not explicitly reported to me ?
Maybe there should be a fourth "code" window on the first post of [URL="https://www.mersenneforum.org/showthread.php?t=27659"]this thread[/URL].
And in this window, everyone could add the sequences they have completed with their acronyms.
And the only person who would remove the sequences from this window would be me, as the sequences are updated on the page.
Here is an example of such a window (XXX, YYY, TTT are the acronyms for the attributions) :
[CODE]3^323: XXX
3^329: XXX
3^331: XXX
5^219: YYY
5^221: YYY
5^223: TTT
6^202: XXX
...
[/CODE]But I don't know if it is possible to allow everyone to make changes in a code window of a post ?

EdH 2022-04-13 13:22

I didn't know how you were updating the tables, which was why I brought up these primes. The current db limiting is definitely an issue. I don't have a solution, but I can offer a couple thoughts and maybe some help from my end, later in this post.

As to the new primes in particular, I haven't been tracking further than what is in the other thread. Several of these new primes are not claimed by anyone. Perhaps they are finished by the elves, or by someone working elsewhere. Since they're unknown, I suggest letting them be Anonymous. If someone wants credit, they can let us know.

I'll add a fourth code block to the first post in the other thread, with a listing of what primes I show that aren't yet in the tables. I normally run a complete matched parity test against your tables and the db a couple times each day. I can easily add in the creation of a list for the fourth code block. I'll also try to keep track if any are claimed. The primes will be persistent until you update the tables, but that's fine. They can collect there until your next update.

If I'm keeping track of all the matched parity sequences for all the existing tables and we just concern ourselves with table updates for those that terminate for right now (due to db limits), which I can flag as described above, would that lessen some of your work with the rest of the updates?

As to db limits, the only resolution that I can think of would be if logging into the db would have higher limits, or if Markus could do so by IP. I haven't tested to see if limits are different when logged in. As far as I can tell, Markus doesn't frequent the forum any more, but his email is listed on the db imprint page. (The link is at the bottom of all the db pages.) He's been quite responsive to emails. He may have a solution.

garambois 2022-04-14 06:47

[QUOTE=EdH;603903]
I'll add a fourth code block to the first post in the other thread, with a listing of what primes I show that aren't yet in the tables. I normally run a complete matched parity test against your tables and the db a couple times each day. I can easily add in the creation of a list for the fourth code block. I'll also try to keep track if any are claimed. The primes will be persistent until you update the tables, but that's fine. They can collect there until your next update.
[/QUOTE]
Yes, I saw that, see my response in the other thread.
Many, many, many thanks for that !


[QUOTE=EdH;603903]
If I'm keeping track of all the matched parity sequences for all the existing tables and we just concern ourselves with table updates for those that terminate for right now (due to db limits), which I can flag as described above, would that lessen some of your work with the rest of the updates?
[/QUOTE]
This greatly reduces my work of course !
That's what you did with the fourth block, isn't it ?
But as I said in the other thread, you also need to make sure that your own workload doesn't become too much.
Otherwise, we're just moving the problem around.


[QUOTE=EdH;603903]
As to db limits, the only resolution that I can think of would be if logging into the db would have higher limits, or if Markus could do so by IP. I haven't tested to see if limits are different when logged in. As far as I can tell, Markus doesn't frequent the forum any more, but his email is listed on the db imprint page. (The link is at the bottom of all the db pages.) He's been quite responsive to emails. He may have a solution.[/QUOTE]
I'm planning on doing some of these tests in the next little while !


[B]I will update again tomorrow, Friday, most likely :[/B]
- New sequences ended with a prime number with the right attributions, based on what's in the 4th block of the first post in the other thread.
- Planned addition of base 87.

garambois 2022-04-14 07:17

I take the base 113 for initialization.

kar_bon 2022-04-14 13:28

75^89 terminates in a P165

EdH 2022-04-14 14:11

[QUOTE=kar_bon;603965]75^89 terminates in a P165[/QUOTE]Nice one!

garambois 2022-04-15 15:11

Page updated.
Many thanks to all for your help.

[B]Added base : 87.[/B]
[B]Updated bases : 3, 5, 6, 18, 28, 30, 33, 34, 35, 37, 41, 44, 45, 48, 51, 52, 55, 56, 66, 80, 82, 90, 91, 210, 276, 552, 882, 14264, 14536.
[/B]
I would like to take this opportunity to inform you that I will not have access to any computer during the next week.
So I won't be able to answer to any message on the forum !

RichD 2022-04-24 13:05

It looks like bases 119 and 127 might already be initialized (by someone else).

EdH 2022-04-24 14:12

[QUOTE=RichD;604682]It looks like bases 119 and 127 might already be initialized (by someone else).[/QUOTE]127 is reserved by kruoli. I don't know anything about 119.

Happy5214 2022-04-30 05:29

I haven't had much time to dedicate to this subproject, so I'll release base 24. I feel like I'm holding up its progress.

garambois 2022-04-30 10:15

[QUOTE=RichD;604682]It looks like bases 119 and 127 might already be initialized (by someone else).[/QUOTE]
I don't know anything about Base 119 either.
But 119=7*17 is not a prime number.
I will add this base in the next update, if you say it was initialized by an anonymous person.
I also plan to add the bases 85 and 89 initialized by myself.
Then I also plan to update all the bases inventoried by Edwin in the other thread.


[QUOTE=Happy5214;605008]I haven't had much time to dedicate to this subproject, so I'll release base 24. I feel like I'm holding up its progress.[/QUOTE]
OK, so I will release base 24.
Thank you very much Happy !

EdH 2022-05-01 18:42

It looks like someone has initialized base 1058. The sequences through exponent 43 are all prime with the first terms for all the rest through 60 above 130 digits. Maybe that could be added now, as well?

Has anyone mentioned this base before?

garambois 2022-05-01 19:05

OK, I'm almost done with the planned update.
I'll wait until tomorrow to see if anyone claims the 1058 base.
So I will add this base tomorrow as well.
Thanks a lot Edwin !

Happy5214 2022-05-01 20:04

1058 = 2*23^2, the next double of a square, so maybe look for that?

garambois 2022-05-02 07:55

[QUOTE=Happy5214;605085]1058 = 2*23^2, the next double of a square, so maybe look for that?[/QUOTE]
Yes, but the question is : Who made these calculations ?
If there is no answer, I will put everything in anonymous "A".

RichD 2022-05-02 13:06

Initializing base 131 next.

Happy5214 2022-05-02 13:23

[QUOTE=garambois;605112]Yes, but the question is : Who made these calculations ?
If there is no answer, I will put everything in anonymous "A".[/QUOTE]
I was hoping that factorization could be useful as a search term. The sequences appear to have been added in early February (around the 7th to the 8th), but no mention of that base was made in this thread around that time. I don't know if those dates jog anyone's memory.

garambois 2022-05-02 13:59

[QUOTE=Happy5214;605122]I was hoping that factorization could be useful as a search term. The sequences appear to have been added in early February (around the 7th to the 8th), but no mention of that base was made in this thread around that time. I don't know if those dates jog anyone's memory.[/QUOTE]
This is really not a big deal.
Whether or not we know the identity of the person who made the calculations, the data will have the same utility.
The person who made the calculations can always come forward later.

garambois 2022-05-02 14:01

[QUOTE=RichD;605121]Initializing base 131 next.[/QUOTE]
OK, many thanks RichD !
As for me, I'm starting to initialize bases 137 and 8191.

garambois 2022-05-02 15:57

Page updated.
Many thanks to all for your help.

[B]Added bases : 85, 89, 119, 1058.[/B]
[B]Updated bases : All those announced in the other thread.[/B]

On our page, all bases are listed exhaustively up to base 101 now.
Also, all bases that are prime numbers are listed up to 103 now.
Bases 119 and 1058 have not been claimed by anyone, so all their sequences are noted as having been computed by anonymous people !
Many bases have all their matched parity sequences in green !

What a colossal work accomplished lately !

EdH 2022-05-02 17:46

All good news! The new bases have even supplied a few more sequences for the other thread.

I see you found another matched parity sequence (85^3) that takes off open-ended. I think we're up to five known, now.

I think I will be adding in the mixed parity sequences for the double square bases that aren't all green to the other thread, since they should also terminate.

Stargate38 2022-05-02 20:07

Could you please put me as the one who did 1058? I terminated it up to i=43, and ran 1058^44 up to i6. I stopped at the C125, as I need to catch up on factoring other numbers on the DB that I had bookmarked from the past few years.

Stargate38 2022-05-02 22:30

Is it possible for an even sequence to hit a square over 100 digits, change parity, and hit another square around 20-40 digits after a few terms? I've been thinking about this for the past month, and I'm wondering if it's even possible, and if so, what the probability is.

garambois 2022-05-03 08:17

[QUOTE=Stargate38;605142]Could you please put me as the one who did 1058? I terminated it up to i=43, and ran 1058^44 up to i6. I stopped at the C125, as I need to catch up on factoring other numbers on the DB that I had bookmarked from the past few years.[/QUOTE]
OK, I will change the attribution for base 1058 in the next update.
Thanks Stargate38.
Is the acronym "STA" appropriate for you to identify yourself as a contributor ?


[QUOTE=Stargate38;605146]Is it possible for an even sequence to hit a square over 100 digits, change parity, and hit another square around 20-40 digits after a few terms? I've been thinking about this for the past month, and I'm wondering if it's even possible, and if so, what the probability is.[/QUOTE]
Have you found such a sequence that does what you describe ?
It would be quite exceptional in my opinion, because the probability of getting on a perfect square or a double of a perfect square and so to change parity is on the order of 1/sqrt(n).

garambois 2022-05-03 12:33

[QUOTE=EdH;605141]All good news! The new bases have even supplied a few more sequences for the other thread.
[/QUOTE]
Yes, a few more sequences.
I'm still thinking of initializing some bases that are prime numbers by next summer, also with the help of RichD or maybe even other volunteers.


[QUOTE=EdH;605141]
I see you found another matched parity sequence (85^3) that takes off open-ended. I think we're up to five known, now.
[/QUOTE]
Yes, we now have a small collection of such initially rare phenomena.
It is also becoming rarer to find new sequences that end in cycles : we have been lucky with bases 85 and 119.


[QUOTE=EdH;605141]
I think I will be adding in the mixed parity sequences for the double square bases that aren't all green to the other thread, since they should also terminate.[/QUOTE]
This is a really good idea.
Maybe we should even add a few more bases that are doubles of squares !

EdH 2022-05-03 13:55

[QUOTE=garambois;605171]. . .
Maybe we should even add a few more bases that are doubles of squares ![/QUOTE]That's how I discovered 1058 was initialized. I was looking at the next couple.

The work for the other thread is slowing quite a bit now. The list has really diminished. I only add a base to my overall list after you've added a table and then only sequences that aren't reserved are included in my lists.

Stargate38 2022-05-03 15:27

I would like to have my acronym be SG1, after the team of the same name from Stargate SG-1.

As for parity-changing sequences, I haven't found such a sequence yet, but I've run thousands of Aliquot sequences with starting values >3*10^6 in an attempt to find one. Not all of them are on the DB, but I've been gradually adding them at a rate that won't flood it.

RichD 2022-05-06 18:50

Base 131 is ready and can be added at the next update.

Taking bases 139 & 149 for initialization next.

RichD 2022-05-08 01:56

Base 139 can be added at the next update.

garambois 2022-05-08 17:45

Page updated.
Many thanks to all for your help.

[B]Added bases : 131, 139, 1152, 1250.[/B]
[B]Updated bases : All the bases announced below.[/B]

For the 1152 base, maybe I was supposed to assign exponents 26 to 36 to Edwin, right ?
The calculations for these exponents had not yet been carried over to the fourth table in the first post of the other thread when I copied it.

[CODE]15^125: Prime - ALF
18^138: Prime - A
19^117: Prime - A
34^96: Prime - A
42^94: Prime - A
46^88: Prime - A
51^87: Prime - A
54^86: Prime - A
55^89: Prime - A
57^83: Prime - A
59^85: Prime - A
61^89: Prime - A
62^86: Prime - A
68^80: Prime - A
69^79: Prime - A
72^90: Prime - EDH
74^78: Prime - A
74^80: Prime - A
82^76: Prime - A
84^76: Prime - A
85^71: Prime - A
85^73: Prime - A
85^75: Prime - A
86^76: Prime - A
89^73: Prime - A
89^75: Prime - A
89^77: Prime - A
92^74: Prime - A
93^75: Prime - UNC
96^74: Prime - A
119^69: Prime - A
119^71: Prime - A
119^73: Prime - A
200^63: Prime - UNC
200^64: Prime - UNC
200^67: Prime - A
284^60: Prime - A
648^51: Prime - A
720^48: Prime - RCH
770^52: Prime - A
882^49: Prime - A
1058^44: Prime - A
1058^45: Prime - A
1058^46: Prime - A
1058^47: Prime - A
1058^49: Prime - A
1152^1: Prime - A
1152^2: Prime - A
1152^3: Prime - A
1152^4: Prime - A
1152^5: Prime - A
1152^6: Prime - A
1152^7: Prime - A
1152^8: Prime - A
1152^9: Prime - A
1152^10: Prime - A
1152^11: Prime - A
1152^12: Prime - A
1152^13: Prime - A
1152^14: Prime - A
1152^15: Prime - A
1152^16: Prime - A
1152^17: Prime - EDH
1152^18: Prime - EDH
1152^19: Prime - EDH
1152^20: Prime - EDH
1152^21: Prime - EDH
1152^22: Prime - EDH
1152^23: Prime - EDH
1152^24: Prime - EDH
1152^25: Prime - EDH
1250^1: Prime - A
1250^2: Prime - A
1250^3: Prime - A
1250^4: Prime - A
1250^5: Prime - A
1250^6: Prime - A
1250^7: Prime - A
1250^8: Prime - A
1250^9: Prime - A
1250^10: Prime - A
1250^11: Prime - A
1250^12: Prime - A
1250^13: Prime - A
1250^14: Prime - A
1250^15: Prime - A
1250^16: Prime - EDH
1250^17: Prime - EDH
1250^18: Prime - EDH
1250^19: Prime - EDH
1250^20: Prime - EDH
1250^21: Prime - EDH
1250^22: Prime - EDH
1250^23: Prime - EDH
1250^24: Prime - EDH
1250^25: Prime - EDH
1250^28: Prime - A
15472^38: Prime - A
[/CODE]

EdH 2022-05-08 18:08

[QUOTE=garambois;605485]. . .
For the 1152 base, maybe I was supposed to assign exponents 26 to 36 to Edwin, right ?
. . .[/QUOTE]Nope! I left those for others and I see they are being worked, but I don't know by whom. It is good to see them being terminated, though. I appreciate the effort from everyone. If 1152 and 1250 run down quickly, it will encourage me to add some more double squares.

Thanks Jean-Luc!

garambois 2022-05-08 18:30

[QUOTE=EdH;605487]If 1152 and 1250 run down quickly, it will encourage me to add some more double squares.
[/QUOTE]
This is really very, very good news !
Really excellent !

:smile:

RichD 2022-05-09 10:37

Base 149 can be added at the next update. Took it to exponent 90.

Reserving bases 151, 157, 163 and 167 next.

garambois 2022-05-09 17:13

Thanks a lot RichD !

garambois 2022-05-11 07:14

Reserving bases 173 and 179.

RichD 2022-05-11 14:12

Bases 151 & 157 can be added at the next update.

garambois 2022-05-11 14:42

[QUOTE=RichD;605668]Bases 151 & 157 can be added at the next update.[/QUOTE]
Up to exponent 90 too ?

And for bases 163 and 167 also up to exponent 90 ?

RichD 2022-05-11 15:47

[QUOTE=garambois;605670]Up to exponent 90 too ?

And for bases 163 and 167 also up to exponent 90 ?[/QUOTE]
Yes, exponent 90 for the completed ones. Base 162 shows max exponent 85 so I will do the same for 163 & 167.


Edit: Oops, I double-checked and base 162 goes to 80. I've already touched exponent 85 if you would like to included the few extras.

garambois 2022-05-11 17:58

[QUOTE=RichD;605677]Yes, exponent 90 for the completed ones. Base 162 shows max exponent 85 so I will do the same for 163 & 167.


Edit: Oops, I double-checked and base 162 goes to 80. I've already touched exponent 85 if you would like to included the few extras.[/QUOTE]
You can go to exponent 85 for bases 163 and 167.
I will extend base 162 to exponent 85 as well.
Many thanks !

RichD 2022-05-15 03:00

Base 163 & 167 can be added at the next update.

I will skip base 181, maybe others will tackle it.
I'll take the 190's, bases 191, 193, 197 and 199 next.

garambois 2022-05-15 10:51

Page updated.
Many thanks to all for your help.

[B]Added bases : 107, 149, 151, 157, 163, 167.[/B]
[B]Extended base : base 162, add exponents 81 to 85.
[/B][B]Updated bases : All the bases announced below.
[/B][CODE]11^157: Prime - A *
15^127: Prime - A *
15^129: Prime - A *
34^98: Prime - A *
44^90: Prime - A *
45^91: Prime - A *
52^88: Prime - A *
59^89: Prime - A *
60^84: Prime - A *
62^84: Prime - A *
66^86: Prime - A *
69^81: Prime - A *
74^82: Prime - A *
89^69: Prime - BIR *
89^79: Prime - EDH *
89^91: Prime - A *
99^75: Prime - UNC *
103^75: Prime - GDB *
139^59: Prime - A *
139^61: Prime - A *
200^65: Prime - EDH (I prodded the elves.) *
882^50: Prime - A *
1058^48: Prime - A *
1152^38: Prime - GDB *
1250^26: Prime - SG1 *
1250^27: Prime - SG1 *
1250^29: Prime - A *
1250^30: Prime - A *
1250^31: Prime - A *
1250^32: Prime - A *
1250^35: Prime - GDB *
1250^37: Prime - GDB *[/CODE]

RichD 2022-05-20 02:39

Bases 191 & 193 can be added at the next update.

garambois 2022-05-22 10:09

Page updated.
Many thanks to all for your help.

[B]Added bases : 191, 193.[/B]
[B]Updated bases : All the bases announced below.[/B]

[CODE]10^150: Prime - UNC *
12^140: Prime - UNC *
19^137: Prime - A *
75^81: Prime - A *
82^78: Prime - A *
107^67: Prime - A *
107^75: Prime - GDB *
131^69: Prime - A *
131^73: Prime - GDB *
139^71: Prime - GDB *
149^57: Prime - GDB *
149^65: Prime - GDB *
149^67: Prime - GDB *
151^59: Prime - GDB *
151^71: Prime - GDB *
157^59: Prime - GDB *
157^65: Prime - GDB *
163^59: Prime - GDB *
163^67: Prime - A *
163^89: Prime - A *
167^59: Prime - GDB *
167^65: Prime - GDB *
167^67: Prime - GDB *
167^71: Prime - A *
167^89: Prime - A *
1152^37: Prime - GDB *
1152^39: Prime - GDB *
1152^40: Prime - GDB *
1152^41: Prime - GDB *
1250^36: Prime - A *
1250^38: Prime - GDB *
1250^39: Prime - GDB *
2310^46: Prime - A *
14316^36: Prime - GDB *[/CODE]

RichD 2022-05-24 00:09

Bases 197 & 199 can be added at the next update.

garambois 2022-05-29 11:03

Page updated.
Many thanks to all for your help.

[B]Added bases : 109, 113, 197, 199.[/B]
[B]Updated bases : All the bases announced below.[/B]

[CODE]6^198: Prime - UNC *
38^100: Prime - GDB *
46^90: Prime - A *
59^87: Prime - GDB *
84^78: Prime - A *
103^77: Prime - GDB *
103^83: Prime - GDB *
119^75: Prime - GDB *
139^69: Prime - A *
157^69: Prime - A *
167^57: Prime - RCH *
167^63: Prime - RCH *
191^55: Prime - GDB *
191^57: Prime - GDB *
193^55: Prime - GDB *
193^59: Prime - GDB *
193^73: Prime - GDB *
220^64: Prime - A *
276^62: Prime - RCH *
648^53: Prime - A *
966^50: Prime - A *
1152^47: Prime - A *
1250^41: Prime - GDB *
15472^36: Prime - GDB *
30030^34: Prime - GDB *[/CODE]

garambois 2022-06-06 19:04

Page updated.
Many thanks to all for your help.

[B]Added bases : 173, 8191.[/B]
[B]Updated bases : All the bases announced below and some others.[/B]
[CODE]6^200: Prime - RCH *
6^206: Prime - GDB *
6^208: Prime - GDB *
10^152: Prime - GDB *
14^136: Prime - A *
45^93: Prime - A *
47^93: Prime - GDB *
53^99: Prime - RCH *
56^86: Prime - GDB *
57^85: Prime - RCH *
60^86: Prime - A *
75^83: Prime - GDB *
85^79: Prime - GDB *
86^78: Prime - GDB *
95^77: Prime - GDB *
109^71: Prime - GDB *
113^71: Prime - GDB *
131^71: Prime - GDB *
139^57: Prime - GDB *
139^67: Prime - GDB *
139^83: Prime - GDB *
149^59: Prime - RCH *
149^69: Prime - GDB *
151^57: Prime - GDB *
151^61: Prime - GDB *
157^57: Prime - GDB *
157^67: Prime - GDB *
193^57: Prime - GDB *
193^61: Prime - RCH *
197^55: Prime - GDB *
197^57: Prime - GDB *
197^59: Prime - GDB *
197^61: Prime - GDB *
199^55: Prime - GDB *
199^59: Prime - GDB *
199^61: Prime - GDB *
564^54: Prime - GDB *
660^54: Prime - GDB *
1152^48: Prime - GDB *
1250^40: Prime - GDB *
1250^42: Prime - GDB *
1250^43: Prime - GDB *
12496^36: Prime - GDB *[/CODE]

gd_barnes 2022-06-09 07:11

87^71 terminates

EdH 2022-06-09 12:27

[QUOTE=gd_barnes;607407]87^71 terminates[/QUOTE]I wonder why I don't have base 87 in my list for the "easier" thread.

I'll add it today.

EdH 2022-06-09 12:46

[STRIKE]Curiosity: Is base 102 being initialized or has it been skipped for some reason I'm not catching?

Edit: I guess several near 102, 104, 106 were skipped for some reason?[/STRIKE]

I guess that just happens to be where our sequencial work has reached. . . Sorry for the bother. . . I'll go back to my other play.:smile:

garambois 2022-06-09 16:59

[QUOTE=EdH;607421][STRIKE]Curiosity: Is base 102 being initialized or has it been skipped for some reason I'm not catching?

Edit: I guess several near 102, 104, 106 were skipped for some reason?[/STRIKE]

I guess that just happens to be where our sequencial work has reached. . . Sorry for the bother. . . I'll go back to my other play.:smile:[/QUOTE]


The bases 102, 104, 106... have not been intialized until now, because we have privileged the bases that are prime numbers in view of the work of this summer 2022 that is coming.
But maybe we will have interesting things when we initialize them.

Otherwise, as you may have noticed, I have initiated the initialization of the bases 1210 and 1184, two amicable numbers and also the base 1264460, a 4-cycle number.

I'm really curious to see what my analysis programs will show me this summer with all this new data !

EdH 2022-06-09 17:38

[QUOTE=garambois;607450]The bases 102, 104, 106... have not been intialized until now, because we have privileged the bases that are prime numbers in view of the work of this summer 2022 that is coming.
But maybe we will have interesting things when we initialize them.

Otherwise, as you may have noticed, I have initiated the initialization of the bases 1210 and 1184, two amicable numbers and also the base 1264460, a 4-cycle number.

I'm really curious to see what my analysis programs will show me this summer with all this new data ![/QUOTE]Thanks! I, too, am looking forward to what might be revealed (especially in the terminations realm*).

* I've done some small scale testing of prime relative things, but nothing that would scale up to such a sizeable study as would be needed. And, nothing that has proved of interest, yet.

garambois 2022-06-09 19:00

[QUOTE=EdH;607455]Thanks! I, too, am looking forward to what might be revealed (especially in the terminations realm*).

* I've done some small scale testing of prime relative things, but nothing that would scale up to such a sizeable study as would be needed. And, nothing that has proved of interest, yet.[/QUOTE]

Have you embarked on a data analysis ?
How did you proceed ?
Did you do something similar to what is described in the [URL="https://www.mersenneforum.org/showpost.php?p=592117&postcount=1360"]post 1360[/URL] ?

EdH 2022-06-09 23:47

[QUOTE=garambois;607462]Have you embarked on a data analysis ?
How did you proceed ?
Did you do something similar to what is described in the [URL="https://www.mersenneforum.org/showpost.php?p=592117&postcount=1360"]post 1360[/URL] ?[/QUOTE]Not really anything extensive and instead of working with prime terminations, I was looking at frequencies of primes within sequences and bases. I never got anywhere significant, though.

garambois 2022-06-10 17:08

[QUOTE=EdH;607477]I never got anywhere significant, though.[/QUOTE]
I have the same problem : it's really hard to know from which angle to attack the problem.
But for several months now, I've been convinced that it's with the method exposed in post #1360 that I have the best chance to find something.
For this summer, we have all the bases exhaustively up to 100 and all the bases that are prime numbers up to 200, because I will finish my initializations very quickly.
This is really better than what we had a year ago !
But it is mostly the sequences that end in primes < 200 that will be examined with this method.
For larger primes, I will have to look at this in a more "classical" way.
I will also try to examine the unfortunately too rare sequences that end in cycles.
We'll see how it turns out.

gd_barnes 2022-06-11 06:46

Jean-Luc,

Would you consider releasing base 77 odd exponents and base 88 even exponents? I noticed that they haven't had any work in a while.

These are some good sequences that we could pick up and likely terminate fairly quickly in the "Somewhat easier n^i sequences for termination" thread here.

Thank you,
Gary

garambois 2022-06-11 07:31

[QUOTE=gd_barnes;607566]Jean-Luc,

Would you consider releasing base 77 odd exponents and base 88 even exponents? I noticed that they haven't had any work in a while.

These are some good sequences that we could pick up and likely terminate fairly quickly in the "Somewhat easier n^i sequences for termination" thread here.

Thank you,
Gary[/QUOTE]

I no longer do any calculations on base 77 odd exponents and base 88 even exponents.
So you can do them.
I only calculate base 77 even exponents and base 88 odd exponents and I do the calculations up to 125 digits for these two bases, that's why it's so long !
Thanks a lot Gary !

garambois 2022-06-11 07:35

I reserve the base 31704 for initialization (a number of the 28-cycle whose calculations had already been started).

gd_barnes 2022-06-11 07:41

[QUOTE=garambois;607567]I no longer do any calculations on base 77 odd exponents and base 88 even exponents.
So you can do them.
I only calculate base 77 even exponents and base 88 odd exponents and I do the calculations up to 125 digits for these two bases, that's why it's so long !
Thanks a lot Gary ![/QUOTE]
Great! Thanks Jean!

Could you also release base 105 odd exponents? :-) I just now noticed that one.

This will give us a lot of good stuff for easier sequences effort.

garambois 2022-06-11 07:50

The case is exactly the same for base 105.
You can calculate all odd exponents for base 105.

I will remove my reservations for exponents of the same parity as the bases for bases 77, 88, 105 in the next update, so that everything is clearer !

EdH 2022-06-11 16:38

An example of some of my "play:"

I'm looking at prime factors that exist in different tables. I find it interesting that for base 496, there are 37439 primes of size greater than 19 digits, and not a single one is duplicated within all those sequences. In fact, I had to move down to 7 digits to find any, and then there were only 31 duplicates, and no greater than two occurrences in 73k primes

(Of course, there's always the chance that my programs are flawed.)

gd_barnes 2022-06-11 20:18

Kruoli appears to have terminated the following same-parity sequences a couple months ago:

76^66, 76^68, 76^70, 76^72, and 76^74

78^66, 78^68, 78^70, and 78^72

richs 2022-06-11 22:30

I am still working on 385^4, now at i2300 (via main sequence 903872).

garambois 2022-06-12 09:29

Page updated.
Many thanks to all for your help.

[B]Added base : 137.[/B]
[B]Modification of reservations for bases 77, 88 and 105.
[/B][B]Updated bases : All the bases announced below and some others.[/B]

[CODE]5^235: Prime - GDB *
5^237: Prime - GDB *
38^96: Prime - RCH *
39^95: Prime - GDB *
51^89: Prime - GDB *
56^88: Prime - GDB *
60^88: Prime - GDB *
87^71: Prime - GDB *
89^85: Prime - RCH *
90^78: Prime - A *
113^77: Prime - GDB *
131^65: Prime - A *
139^73: Prime - GDB *
163^57: Prime - RCH *
163^65: Prime - GDB *
163^71: Prime - GDB *
167^73: Prime - GDB*
173^67: Prime - GDB *
173^69: Prime - GDB *
191^61: Prime - RCH *
191^67: Prime - GDB *
199^71: Prime - GDB *
200^66: Prime - GDB *
1250^47: Prime - RCH *
8191^39: Prime - EDH *
And some sequences for bases 77, 88 and 109.[/CODE]

garambois 2022-06-12 09:34

[QUOTE=EdH;607593]An example of some of my "play:"

I'm looking at prime factors that exist in different tables. I find it interesting that for base 496, there are 37439 primes of size greater than 19 digits, and not a single one is duplicated within all those sequences. In fact, I had to move down to 7 digits to find any, and then there were only 31 duplicates, and no greater than two occurrences in 73k primes

(Of course, there's always the chance that my programs are flawed.)[/QUOTE]


Is 496 the only base for which this phenomenon is observed, or do all other bases behave in a similar way ?
Have you done this work for all the bases ?

gd_barnes 2022-06-12 10:20

[QUOTE=gd_barnes;607601]Kruoli appears to have terminated the following same-parity sequences a couple months ago:

76^66, 76^68, 76^70, 76^72, and 76^74

78^66, 78^68, 78^70, and 78^72[/QUOTE]
I posted this yesterday. Were they somehow missed in the update? They were terminated ~2 months ago.

garambois 2022-06-12 11:32

[QUOTE=gd_barnes;607627]I posted this yesterday. Were they somehow missed in the update? They were terminated ~2 months ago.[/QUOTE]
Yes, that's right, I forgot about bases 76 and 78, as they are not in the table in the first post.
And there must be others too, I don't know which ones.
I'll update bases 76 and 78 soon and I think in early July I'll even try to update all the bases in the project to make sure I don't forget any.
But the read restrictions of FactorDB won't make it easy for me.

Thanks a lot Gary for your comment !
Please let me know if there are any other omissions or errors, there must still be some.

For example, I also noticed yesterday that the prime 181 was missing from the list of all bases < 200 that are primes. I don't know why we had forgotten 181 ?
I will initialize it.

gd_barnes 2022-06-12 12:20

[QUOTE=garambois;607631]For example, I also noticed yesterday that the prime 181 was missing from the list of all bases < 200 that are primes. I don't know why we had forgotten 181 ?
I will initialize it.[/QUOTE]
Oh! I was not aware that we wanted all prime bases < 200.

That's unfortunate. In addition to base 181, bases 137 and 179 are missing too.

EdH 2022-06-12 12:56

[QUOTE=garambois;607626]Is 496 the only base for which this phenomenon is observed, or do all other bases behave in a similar way ?
Have you done this work for all the bases ?[/QUOTE]I've only tested a few bases and tried 496 because it's a perfect base. I've posted before that the factors for term 1 seem to appear in term 1 of multiples of exponents, but it didn't appear to always be the case. Here's one example for base 3:[code]3^61: 1 . 63586737412824305271441649801 = [B]603901[/B] * [B]105293313660391861035901[/B]
3^122: 1 . 8086546349614940446859309232793222678791640323920329978804 = 2^2 * 367 * [B]603901[/B] * [B]105293313660391861035901[/B] * 86630432442539925437931403
3^183: 1 . 1028394198619196296580411324228310083630734818932335155774021137556921354130946013264613 = 13 * 733 * [B]603901[/B] * 97806913 * 2421854958301 * [B]105293313660391861035901[/B] * 7165195867462155138286987098273769
3^244: 1 . 130784463728941437304366605878791157545446108607097625128287829156986450640585159915213324860247524675186582838498440 = 2^3 * 5 * 367 * 180317 * [B]603901[/B] * 262199473 * 39504363995133913 * [B]105293313660391861035901[/B] * 86630432442539925437931403 * 865923475887669700104067517
3^305: 1 . 16632314705618487682946112326923730389925339018478498531284843094521833157066137806146725047916206378672433859532656276201841797031032036609769121 = 11^2 * 65881 * [B]603901[/B] * 4919054377091 * [B]105293313660391861035901[/B] * 46229214937048975901175732207117334435811 * 144292067692894029928776589038168491785927205865834517921[/code]Extending this past the tables, appears to hold true:[code]3^366: 1 . 2115189255507237924072337092557357070551223108145702025517161642287632777865643495570127933612128865041369784141182974844571230942534643815236048609413759606508669383942608764 = 2^2 * 7 * 13 * 367 * 733 * 189223 * [B]603901[/B] * 97806913 * 279666823 * 6117064141 * 2421854958301 * 109870115206699 * 64961725048119249391 * [B]105293313660391861035901[/B] * 86630432442539925437931403 * 7165195867462155138286987098273769[/code]I've checked a few more in factordb and it held for all I checked.

The prime 105293313660391861035901 did not appear anywhere else in my entire set of sequences for all the tables. (I am still missing a few of the recently added tables.)

Of course, as expected, the prime 603901 appears in over 600 terms throughout the tables.

garambois 2022-06-12 13:01

[QUOTE=gd_barnes;607634]
That's unfortunate. In addition to base 181, bases 137 and 179 are missing too.[/QUOTE]
Sorry, but the base 137 is on the page ! (I just saw that I have to remove it from the list of bases reserved for initialization !)
As for base 179, I've finished its initialization very soon !

I wanted all the bases that are prime < 200 because I'm thinking of doing the work described in [URL="https://www.mersenneforum.org/showpost.php?p=592117&postcount=1360"]post #1360[/URL] for each prime but only with bases and exponents that are also prime.
This is just a hunch, I need to check what it can do !

Of course, several other tests are planned.

EdH 2022-06-12 13:05

[STRIKE]If you want, I can initialize 181. I'll wait for my current number to finish, in case someone else would like to tackle it.[/STRIKE]

Edit: I just noticed you grabbed it!

charybdis 2022-06-12 13:26

[QUOTE=EdH;607636]I've posted before that the factors for term 1 seem to appear in term 1 of multiples of exponents, but it didn't appear to always be the case.[/QUOTE]

If the base b is prime, then term 1 of sequence b^n will be b^(n-1) + b^(n-2) + ... + b + 1 = (b^n-1)/(b-1). Since b^n-1 divides all numbers of the form b^kn-1, this naturally leads to shared factors as you observed. When the base is composite (and not a prime power) there isn't a nice expression for term 1.

EdH 2022-06-12 14:05

[QUOTE=charybdis;607640]If the base b is prime, then term 1 of sequence b^n will be b^(n-1) + b^(n-2) + ... + b + 1 = (b^n-1)/(b-1). Since b^n-1 divides all numbers of the form b^kn-1, this naturally leads to shared factors as you observed. When the base is composite (and not a prime power) there isn't a nice expression for term 1.[/QUOTE]Thank You! This answers a subsequent question I had, involving further multiple exponents. All the factors shown in the above 3^122 term 1, will be present in multiples of 122, but not in other multiples of 61 that aren't multiples of 122.

garambois 2022-06-12 14:08

@Edwin :
This reminds me of work started two years ago.
We were asking ourselves similar questions from post #358 onwards (see also post #364).

@charybdis :
Yes, thank you for pointing out this demonstration, I had noted it at the time.

On the other hand, this kind of research could be really very interesting, indeed, for example if one found the prime number 105293313660391861035901 in another base !
Because the probability to find this same prime number of this size in another base must be almost null.
If we could find it in another base, it would certainly not be due to chance !
So I think we need to do that kind of research.

charybdis 2022-06-12 14:14

The other consequence of the (b^n-1)/(b-1) observation is, of course, that SNFS can be used on term 1 for prime bases.

EdH 2022-06-12 14:22

[QUOTE=garambois;607648]@Edwin :
This reminds me of work started two years ago.
We were asking ourselves similar questions from post #358 onwards (see also post #364).
. . .
[/QUOTE]I'm remembering better now, that it was explained before, but somehow slipped away for a bit as I kept "playing." Thanks for the memory jog. That's why we have notes and places like this forum. It also helps to burn it in when a couple different sources are consulted.

EdH 2022-06-12 14:26

[QUOTE=charybdis;607649]The other consequence of the (b^n-1)/(b-1) observation is, of course, that SNFS can be used on term 1 for prime bases.[/QUOTE]I expected that these would be special cases and therefore had ways to an advantage. A tiny bit more understanding may have been realized today.

garambois 2022-06-12 16:13

[QUOTE=garambois;607648]
On the other hand, this kind of research could be really very interesting, indeed, for example if one found the prime number 105293313660391861035901 in another base !
Because the probability to find this same prime number of this size in another base must be almost null.
If we could find it in another base, it would certainly not be due to chance !
So I think we need to do that kind of research.[/QUOTE]
Since I wrote this passage earlier this afternoon, the idea has been nagging at me !

I can't find any work on this exact point in my archives, nor on the forum !
However, it seems to me that I have already worked on this.
I'll have to look into it this summer.

@Edwin :
Maybe your programs are already written and allow you to do this work ; I'll do the work on my own this summer, but it's always better to be able to check.
Do your programs allow you to answer this kind of query :
"Print on a line the numbers P, B, E, and I for all primes P > 10^9[U] that are found in at least 2 different B bases[/U]." (so there would be at least 2 lines for each P with 2 different Bases with the corresponding E and I specified)
B is the Base of occurrence of P, E the Exponent that indicates in which sequence P is found for this base, and I the Index of occurrence of P in the sequence.
Edwin : Only take this message into account if the program is already written, because I think this is a big and complicated job : Do not spend hours writing this program if it does not already exist !

EdH 2022-06-12 17:58

[QUOTE=garambois;607663]. . .
@Edwin :
Maybe your programs are already written and allow you to do this work ; I'll do the work on my own this summer, but it's always better to be able to check.
Do your programs allow you to answer this kind of query :
"Print on a line the numbers P, B, E, and I for all primes P > 10^9[U] that are found in at least 2 different B bases[/U]." (so there would be at least 2 lines for each P with 2 different Bases with the corresponding E and I specified)
B is the Base of occurrence of P, E the Exponent that indicates in which sequence P is found for this base, and I the Index of occurrence of P in the sequence.
Edwin : Only take this message into account if the program is already written, because I think this is a big and complicated job : Do not spend hours writing this program if it does not already exist ![/QUOTE]This is near where I'm already headed and I think I have, on a small scale, already found some such numbers at larger than 20 digits. I'll try to find that again, to see if my memory is working. I'm pretty sure the prime I'm thinking of was in two of the bases 2, 3 and 5.

As to a larger scale, the volume of primes is so large, it quickly becomes outside program limits. Base 2 has 40605 unique primes larger than 9 digits, but all the sequences in the base 2 table run pretty much straight to termination. Bases with open-ended sequences will collect many more primes. When I ran both bases 2 and 3 together, the total count of unique primes larger than 9 digits climbed to 408116.

kruoli 2022-06-12 18:08

Jean-Luc, you can remove all of my reservations for now since I am currently not working on them anymore (bases 76, 78, 94 and 127) to free them for the other sub-project. It might be necessary to update all of them once, since I did some work that is not yet shown here. Gary mentioned some of those already.

EdH 2022-06-12 18:23

[QUOTE=kruoli;607675]Jean-Luc, you can remove all of my reservations for now since I am currently not working on them anymore (bases 76, 78, 94 and 127) to free them for the other sub-project. It might be necessary to update all of them once, since I did some work that is not yet shown here. Gary mentioned some of those already.[/QUOTE]Once the reservations are lifted, my scripts will work with the db values, so from the perspective of the other thread, the tables don't need actual factordb updating.

garambois 2022-06-12 19:01

[QUOTE=gd_barnes;607627]I posted this yesterday. Were they somehow missed in the update? They were terminated ~2 months ago.[/QUOTE]



[QUOTE=kruoli;607675]Jean-Luc, you can remove all of my reservations for now since I am currently not working on them anymore (bases 76, 78, 94 and 127) to free them for the other sub-project. It might be necessary to update all of them once, since I did some work that is not yet shown here. Gary mentioned some of those already.[/QUOTE]


[B]The announced small update is done : bases 76, 78, 94 and 127 updated.[/B]

A lot of thanks Oliver for your help !

garambois 2022-06-12 19:18

[QUOTE=EdH;607673]This is near where I'm already headed and I think I have, on a small scale, already found some such numbers at larger than 20 digits. I'll try to find that again, to see if my memory is working. I'm pretty sure the prime I'm thinking of was in two of the bases 2, 3 and 5.
[/QUOTE]
20 digits ?
It seems almost unbelievable to me !
I would be really, really interested to know this prime number, the bases involved, the exponent and the indexes, please if you can !


[QUOTE=EdH;607673]
As to a larger scale, the volume of primes is so large, it quickly becomes outside program limits. Base 2 has 40605 unique primes larger than 9 digits, but all the sequences in the base 2 table run pretty much straight to termination. Bases with open-ended sequences will collect many more primes. When I ran both bases 2 and 3 together, the total count of unique primes larger than 9 digits climbed to 408116.[/QUOTE]
I think your point is well taken.
This work is probably not within the reach of our current computers.
This is really a pity.
Because I think that such prime numbers should not be found in the few bases of our project, but it would be better to be able to check it, especially if the indexes exceed 5 or 10 !
I'm really looking forward to see your 20+ digit number.
Or maybe there are trivial cases I haven't thought of !

EdH 2022-06-12 19:20

[QUOTE=EdH;607673]This is near where I'm already headed and I think I have, on a small scale, already found some such numbers at larger than 20 digits. I'll try to find that again, to see if my memory is working. I'm pretty sure the prime I'm thinking of was in two of the bases 2, 3 and 5.
. . .[/QUOTE]I'm beginning to think in all the distracting colors put forth by grep in a terminal, I misinterpreted 2^535 or 2^545 as being 5^---. As to primes larger than 9 digits across multiple bases, I'll get back a little later.

EdH 2022-06-14 00:08

[QUOTE=garambois;607663]. . .
@Edwin :
Maybe your programs are already written and allow you to do this work ; I'll do the work on my own this summer, but it's always better to be able to check.
Do your programs allow you to answer this kind of query :
"Print on a line the numbers P, B, E, and I for all primes P > 10^9[U] that are found in at least 2 different B bases[/U]." (so there would be at least 2 lines for each P with 2 different Bases with the corresponding E and I specified)
B is the Base of occurrence of P, E the Exponent that indicates in which sequence P is found for this base, and I the Index of occurrence of P in the sequence.
Edwin : Only take this message into account if the program is already written, because I think this is a big and complicated job : Do not spend hours writing this program if it does not already exist ![/QUOTE]The following isn't (yet) in the format you described, but it seems to show that at least at 10 digits, many of the primes exist in multiple bases, and at various terms. Here is a very small sampling of a current test run:[code]Prime 3258313481:
2^305:11
24^17:1520
Prime 1129552253:
2^341:25
19^18:510
Prime 2159188693:
2^327:18
50^98:7
Prime 1639132051:
2^422:11
22^41:508
Prime 1051654267:
2^468:58
19^22:2102
Prime 1097038783:
2^501:61
67^83:11[/code]


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