Sequences >1M and < 5M

[ugly2dog]

I have been working on the sequences from 1M to 5M for some time [years].
All the open sequences have been taken to at least 90 digits. I might have missed some though.
Some of the sequences might have dropped below the 90 digit level due to the database workers advancing them.
The number of open sequences [by the best info I can collect] are:
Range Num Length Max Min
1e6-2e6 9513 6326 126 90
2e6-3e6 9526 10398 145 90
3e6-4e6 9647 7298 140 90
4e6-5e6 9685 6940 128 90

The longest sequences for each range are:
1621074:I6326:D115
2005020:I10398:D145
3586440:I7298:D105
4429128:I6940:D116

I am currently working on 2005020, hands off.

I am also trying to advance all the open sequences to 95 digits.
I currently have ~3250 sequences advanced from 90 to 95 digits, ~800 sequences advanced up to 105 digits, ~280 sequences advanced up to 110 digits, that I really need to enter into the db, but I haven't had any spare time in the last couple of months.
There might be a few more merges/terminations in the ones I have yet to enter yet.

I need to download all the sequences below 1M to be able to find the open sequences from 5M to 10M. Polling the db for the information isn't feasible.

If anyone is interested in my current list of open sequences, let me know.

[RichD]

Are there many terminations after reaching say 60, 80 or 100 digits in size?

[ugly2dog]

I can't give exact numbers until I have time to redo my index, again.
Right now I only keep track off the active ones I know that haven't terminated/merged.
From 70 to 80, around 1200 terminated/merged.
From 80 to 90, around 600 terminated/merged.
From 90 to 95, around 100 have terminated/merged so far [still working on this range, ~26000 sequences left to finish this level].
From 95 to 100, around 30 have terminated so far [still working on this range].
From 100 to 105, around 15 have terminated so far [still working on this range].
These don't include sequences that were previously done before I started working on the ranges.

There are ~5000 sequences taken from 90 to 95 digits, ~750 sequences taken from 95 to 100 digits, ~350 sequences taken from 100 to 105 digits, ~100 sequences taken from 105 to 110 digits, that I haven't even looked at, so there should be a few more terminations/merges I haven't found yet.

[RichD]

I wonder if a few dozen low level (meaning small composites) should be opened up for newbies. NFS & GGNFS can be a bit intimidating. Ban the big names from reserving one of these. Let the "For newbies only" run ECM and QS from Msieve or YAFU to get a feel for the processes and the sequences.

It's a step backward in the forum but to cultivate new blood for the future.

P.S. I should ask, are there any open sequences still below say 85-90?
Or should we look at higher sequences?

[henryzz]

Originally Posted by RichD

I wonder if a few dozen low level (meaning small composites) should be opened up for newbies. NFS & GGNFS can be a bit intimidating. Ban the big names from reserving one of these. Let the "For newbies only" run ECM and QS from Msieve or YAFU to get a feel for the processes and the sequences.

It's a step backward in the forum but to cultivate new blood for the future.

P.S. I should ask, are there any open sequences still below say 85-90?
Or should we look at higher sequences?

I have wondered. It would be nice to generate some activity around here again.
If we were to get properly busy I would need help with admin. It is a shame we can't extend dubslow's page to include a larger range.

[ugly2dog]

Everything below 5M has been taken to at least 90 digits, so the composites are less than that for a lot of sequences.
I don't keep track of the next number in the sequence or the drivers.
I do have ~9000 sequences that I have advanced, that I will be entering in the db the next couple of weeks.

The number of sequences are more than 4x times the amount on dubslow's page now. So trying to update them in a timely fashion is not feasible.

Greebley has been working on the sequences 5M-10M. Check his post on this as these ranges have been taken to lower levels.

[garambois]

Originally Posted by ugly2dog

The longest sequences for each range are:
1621074:I6326:D115
2005020:I10398:D145
3586440:I7298:D105
4429128:I6940:D116

I am currently working on 2005020, hands off.

Just for fun, here is an aliquot sequence with over 16000 iterations.

In fact, I calculated the aliquot antecedents of 2005020 of order 1, 2, 3, ...... 1017.
The integer 2005020 has an odd aliquot antecedent which is (2005020-1) ^ 2.

However, each odd number n has an odd aliquot antecedent m = pq such that p + q + 1 = n (if Goldbach conjecture is true), with p and q prime numbers.
It is quite easy to find a pair of prime numbers (p, q), even for n making thousands of digits, taking first p as small as possible and making a primality test on q = n-1-p.
So, I initiated programs that go back for 3, 7, 9 (the same than 3), 11, 13 and 17 and these calculations are in progress.
When I will have prime numbers q with 10000 digits (august or september 2015 ?), I will put my new aliquot sequences on factordb.

[LaurV]

Nice
Did you "prove" the primality for all those 3k-digits numbers? (fdb says they are prp, and it may take some time until the local workers will prove all of them).

[garambois]

Originally Posted by LaurV

Nice
Did you "prove" the primality for all those 3k-digits numbers? (fdb says they are prp, and it may take some time until the local workers will prove all of them).

I didn't really prove the primality for all those 3k-digits. But It is almost certain !
In the software "Sage", we have the test "is_prime(n)" (it proves if n is prime) and a second test "is_pseudoprime(n)" (it is a pseudo-primality test).
When n<=10^500, in my program, I use the first and when n>10^500, I use the second.
But for numbers n>500, the pseudo-primality test is almost certain.
For exemple, for probabilistic Fermat test, for only one value of a, E(10^500)<2.3*10^(-55), and E(10^1000)<1.2*10^(-123).
E(n) is the risk of error for n.
And I tried with "is_pseudoprime" for small values of n too, no problem. But in my program, I have taken more precaution, as said above.
With only the test "is_prime(n)", it is impossible to test a lot of integers whith more than 2000 digits in a "reasonable" time !

[pakaran]

Does anyone know if there's a way to search for sequences that are still open?

[ChristianB]

Originally Posted by pakaran

Does anyone know if there's a way to search for sequences that are still open?

We could do the same as for sequences <1M here: http://www.rechenkraft.net/aliquot/AllSeq.html either extend the current page or set up a new page.

But usually you would check with factordb: http://factordb.com/sequences.php.