Let's see what happens this time. Again below 120 digits with the down-driver. :rolleyes:

Well, with the same notation as before, say t=2*F, then its s is 3(1-F*)-2F, therefore this can never be multiple of 3. To "break", it needs to change the power of 2, and that is only possible if F=Qp is a product of an odd perfect square Q and a prime p with p=1 mod 4. It also works if p or q are void. For that to happen below 100 digits the chances (i.e. bad odds) are:

at ~50 digits: below 1%
at ~40 digits: below 1.6%
at ~30 digits: about 2.4%
at ~20 digits: about 3.6%
at ~15 digits: about 4.8%
at ~10 digits: about 7.2%

We are "safe" for now :razz: (yeah, well, I know, "don't jinx it!" hehe).

< 100 digits again!

Booooooooooooooooooo. i8359 = 2 * 7^2 * P91

[QUOTE=Dubslow;442507]Booooooooooooooooooo. i8359 = 2 * 7^2 * P91[/QUOTE]

yeah but luckily since sigma(2^3) = 15 we would need a factor of 3 or 5 to drive it up at last check of what's been said. okay now it's is 2^2 and so would need a 7 I think. and now at 90 digits and a single 2.

[QUOTE=science_man_88;442509]and now at 90 digits and a single 2.[/QUOTE]

Huzzah!
[code]
Checked 8417 93 (show) 2687306884...12<93> = 2^2 · 3^4 · 8294157051...13<90>
[/code]
[$]\tau(P90) = 1[/$] and we have recovered the downdriver!

Down below 90! 86 and dropping, now 81. We're at the point where the DB is factoring most of the lines by itself.

[QUOTE=science_man_88;442509]yeah but luckily since sigma(2^3) = 15 we would need a factor of 3 or 5 to drive it up at last check of what's been said. okay now it's is 2^2 and so would need a 7 I think. [/QUOTE]

Yeah these are/were correct.

Edit: 1205Z and I got a refresh down at 37 digits, subsequent refresh attempts are still pending. Exciting! Termination or more disappointment?

[QUOTE=Dubslow;442510]Huzzah!
[code]
Checked 8417 93 (show) 2687306884...12<93> = 2^2 · 3^4 · 8294157051...13<90>
[/code]
[$]\tau(P90) = 1[/$] and we have recovered the downdriver![/QUOTE]
we are about i8433 right now actually. i8458 is this going to be like yesterday where I couldn't keep up with the edit needed to keep it recent lol. edit: yeah probably ... now at or above i8507. and around 74 digits. might update this edit near my end of edit time. driver:2^4*31 now back at over 90 digits and climbing.

314718 just passed i15,000.

Even though it's a bit (but not extremely) unlikely that the sequence will terminate soon and it's very unlikely that the sequence will catch itself on the way down to create a large cycle, I don't think the probability of those events are in "winning the lottery" territory, and it certainly wouldn't be like the coin flips in Tom Stoppard's "Rosencrantz and Guildenstern Are Dead" at [URL]https://youtu.be/KchhSIVwMdY?t=1m30s[/URL] .

Nope, 1208Z and the downdriver went below 20, cycled up to 50 then below 20 again and now back into the 80s with the D4 = 2^4 * 31. Close to 1500 lines added in the last 30 minutes. Edit: 1210Z and we have passed 10,000 total lines! Congrats Ryan, better than nothing :razz:

10000 lines and counting! 2^4*31 isn't easy to survive.

102 digits now i10133 1700 iterations from when I posted in response to dubslow. and 66 minutes roughly. average of roughly 2.33 seconds per iteration roughly. ( to within a minute timing total).