A084598 & A084599, factorization

[all at abouthugo.de]

Marc LeBrun <mlb at fxpt.com> schrieb am 02.06.2003, 17:57:11:
>  > Hugo Pfoertner 
>  > (What you computed was the smallest factor contradicting the
>  > given description saying _largest_)
> 
> Hugo,
> 
> Doh!  There was a stupid bug in my code that was recycling old "memoized" 
> values from the previous sequence.  Should've thought for a microsecond longer!
> 
> Many thanks for correcting this and extending the sequences to full length!

Marc, it was fun (and some cut and paste work) to
extend the sequences. For A084599 I've found one
more term:
2*3*5*29*79*68729*3739*6221191*157170297801581*70724343608203457341903*
46316297682014731387158877659877*78592684042614093322289223662773*
181891012640244955605725966274974474087-1=
11 x 204249779 x 657690574770645301 x 

547275580337664165337990140111772164867508038795347198579326533639132704344301831464707648235639448747816483406685904347568344407941
(132 digits)

Plugging this back into the product we get
the factorization:
13 x 67 x 14479 x 167197 (Curve 1) x 
924769 x 2688 244927 (Curve 2) x 888838 110930 755119 (Curve 38) x 94990

039787 558533 628054 698185 745479 080770 094049 594768 708357 751479
834472 
271418 740615 811262 963326 395526 626301 118890 552246 833453 772134
451411 
165820 049808 382687 685256 717639 444505 759325 777974 394137 687184
854183 
590802 465536 646278 398648 699248 975631 698109 (Composite), where the
composite has 247 digits.
If we are not very lucky, then this is the end of
the game (I ran ECM for two days, saying smallest
factor probably > 10^30).

This brings me to a more general question:
There are many sequences, whose extension is
only possible with either break-throughs in
factorization algorithms or using massive
computer power. Do we have something like an
index identifying all sequences dependent on
factorization? The best would be to have a
keyword "primfac" or something similar, 
but this is maybe a little too bold from my side.
A somewhat similar situation occurs for sequences
dependent on primality testing. Also here an
index or even keyword "primtes" would be helpful.

Just an idea ...

Hugo