Aliquot sequences that start on the integer powers n^i

[EdH]

Everything is looking great from my perspective and I've added the new bases to the other thread, although for the near time I won't do any work above base 20 for the other thread.

Thanks for all the work. I hope we aren't giving you too much with the other thread.

Edit: 24^110 is still being carried in the other thread and shouldn't be lost, so it shouldn't be an issue to let it stay there from my viewpoint.

[gd_barnes]

Originally Posted by EdH

Edit: 24^110 is still being carried in the other thread and shouldn't be lost, so it shouldn't be an issue to let it stay there from my viewpoint.

Sound great to me!

Right now with the same-parity exponents, if a base has been initialized here but does not show on the web page -or- you have not had time to include it in your listings in the other thread, I'll report any termination here. If it is shown on the web page and in your listing, of course I'll report it there.

[garambois]

Originally Posted by EdH

Right now my primes list for >10^9, which is uniques* for each base and multiples across is 331.3 MB, with 9615120 primes.

Whittled down to multiples across two+ bases, that list is 6.5MB, with 174161 primes, but most of those are due to merges.

* in this case unique means a prime is represented only once for a base, even though it shows up multiple times within that base. As of yet, I haven't noticed any primes that show up multiple times within a single base AND within another base.

WOW, this is heavy stuff !
But I think once the mergers are removed, the quantity will decrease a lot, at least if you can do that !

Originally Posted by gd_barnes

Oops. You are correct. I was looking at 48^82. I get that mixed up all the time. Mea culpa. :-)

I also make this kind of mistake regularly !
;-)

Originally Posted by EdH

Thanks for all the work. I hope we aren't giving you too much with the other thread.

It's great if I have work, it means we are making progress.
It's just that I can't always do the updates right away and sometimes it takes 10 or 15 days or even more depending on the period.

[EdH]

Here's a full list of all primes >10^9 that occur in two bases, with all merges reflected only once. This listing does not include the most current bases, but otherwise includes the entire set of tables. In the case where a prime was found in several merged sequences, only one of the merged sequences is listed. This list is for all multiples >10^9. Of note, I don't believe there are any triples and there are no examples larger than 12 digits. Here are the 12 digit primes:

109964639887,193,22,263
109964639887,40,19,182
126249927637,15472,5,113
126249927637,67,75,5
142754777149,101,32,504
142754777149,52,39,640
154198251007,17,76,702
154198251007,22,87,1336
194041181491,439,22,392
194041181491,76,35,2974
220689850709,12496,19,494
220689850709,15,12,3377
389689791443,10,109,4650
389689791443,15,34,1318
392293758937,10,85,807
392293758937,42,23,2984

[RichD]

Bases 239 & 241 can be added at the next update.

[garambois]

Originally Posted by RichD

Bases 239 & 241 can be added at the next update.

OK, many thanks Rich !

[garambois]

Originally Posted by EdH

Here's a full list of all primes >10^9 that occur in two bases, with all merges reflected only once. This listing does not include the most current bases, but otherwise includes the entire set of tables. In the case where a prime was found in several merged sequences, only one of the merged sequences is listed. This list is for all multiples >10^9. Of note, I don't believe there are any triples and there are no examples larger than 12 digits. Here are the 12 digit primes:

109964639887,193,22,263
109964639887,40,19,182
...
392293758937,10,85,807
392293758937,42,23,2984

Thank you very much Edwin.
This time, everything seems to be perfect.
I did several checks, everything is good.
I will do some more analysis in 2 weeks.
A priori, the occurrences of these primes seem to be completely random.
I will have to be creative to try to find something else, I will look, even if I think that there should be nothing else than random.
I will also try to find these lists with my own program, to confirm them.
I remember that more than two years ago you sent us lists that you had obtained with other programs.
And it was only a year later that I noticed something that led to a conjecture.
So we will have to be patient !

[gd_barnes]

I have terminated the following same-parity sequences:

239^53, 239^55, 239^57, 239^63, & 239^67
241^53, 241^55, 241^57, & 241^59

[Happy5214]

It's been a while, but I'm assuming the inclusion standard for a base is still initializing everything to 100 digits. If that's the case, base 306 (306:i1=396=276:i1, so this falls under the "merges into open" category) can be added. Its same-parity sequences are actually terminated up to 140 digits thanks to some lucky ECM hits.

After some personal Riesel assignments, I'll resume base 210 at 210^9 (210^5 and 210^7 have reached C120+ cofactors, so I'm done with those).

[garambois]

Originally Posted by Happy5214

It's been a while, but I'm assuming the inclusion standard for a base is still initializing everything to 100 digits. If that's the case, base 306 (306:i1=396=276:i1, so this falls under the "merges into open" category) can be added. Its same-parity sequences are actually terminated up to 140 digits thanks to some lucky ECM hits.

If I understand correctly, you have initialized the base 306, right ?

[gd_barnes]

Originally Posted by Happy5214

It's been a while, but I'm assuming the inclusion standard for a base is still initializing everything to 100 digits. If that's the case, base 306 (306:i1=396=276:i1, so this falls under the "merges into open" category) can be added. Its same-parity sequences are actually terminated up to 140 digits thanks to some lucky ECM hits.

I have recently been following up on newly initialized bases by doing additional work on (only) same-parity sequences up to 160 digits. If it's OK with you, I'd like to do that here for those in the 140-160 digit range.