I can break or bend at least #3, #4, #5, #6, #7, and #19 on your newest list. (Not that you need to care about what trivialities I can dredge up, of course.) I'm still fundamentally opposed to #20: why encourage people to harm the environment by using more electricity than needed to prove a prime? And why wouldn't they just cheat and use a newer program?

For #18, I take it that this means that neither factor is one of #1-#15?

#16 looks cool.

[QUOTE=3.14159;227378]No patterns in any section of digits.
No predictable sequences.
Statistically likely.

Don't those stand out to you as the characteristics of a randomly-chosen number?[/QUOTE]

Is 4584747435685437658437 such a number? How do you know? What about [code]17935520800145983429475264219083132046283745750116734433889605552003293726651449435812688477850840442133972456012956887645193084972760632253129406[/code]
? What about 2665124305184977723311826852179758605262374940671173169012746835211677949?

[QUOTE=3.14159;227380]A demonstration of how easy it is to find a large special-form cofactor: [/QUOTE]

I think I showed that in #969 and #973 well enough. :smile:

[QUOTE=3.14159;227380]Yes, yes, fuse them into Generalized. But Generalized is not inclusive to factorial/primorial/prime numbers. Updating.
Same for the rest.[/QUOTE]

I can still bend/break #3, #4, #5, #6, #7, and #19. #8 isn't hard either; #2 is largely but not entirely fixed by the change. #19 has at least two trivial vulnerabilities, but it almost doesn't count since the worst vulnerability you already know about and have declined to change/fix.

[QUOTE=CRGreathouse]I can still bend/break #3, #4, #5, #6, #7, and #19. #8 isn't hard either; #2 is largely but not entirely fixed by the change. #19 has at least two trivial vulnerabilities, but it almost doesn't count since the worst vulnerability you already know about and have declined to change/fix.
[/QUOTE]

3: Nothing wrong with it: The only thing you keep complaining about is fusing it into Generalized.
4: Same as 3.
5: Same as 4.
6: Yes, this does not stand to the true definition of primorial prime.
7: Same as 6.
19: 10^k + c and something else.

[QUOTE=3.14159;227384]3: Nothing wrong with it: The only thing you keep complaining about is fusing it into Generalized.[/QUOTE]

Actually, I've never complained about that or found it to be a vulnerability. I have a better break in mind.

[QUOTE=3.14159;227384]19: 10^k + c and something else.[/QUOTE]

Why would I want to use that?


Any response to #993?

[QUOTE=CRGreathouse]Actually, I've never complained about that or found it to be a vulnerability. I have a better break in mind.
[/QUOTE]

Invalid, same restrictions apply to those as they do to proths, k < b[sup]n[/sup].

[QUOTE=CRGreathouse]Why would I want to use that?
[/QUOTE]

Every number greater than 10^1999+100 can be expressed as such. Is this ever going to end?

[QUOTE=CRGreathouse]Any response to #993?
[/QUOTE]

Nothing to respond to in Post 993.

If there is any weird/distorted/strange crap, ask mods to remove it, please. The network is failing me, and my posts tend to be mangled when network failure occurs during me typing a post.

Here's one for categories #2 and #19:

[I]Start: For n=18778 to 18778, For k=494 to 494 step 2, k*288^n+1.[/I]
[I]494*288^18778 + 1 may be prime. (a = 2)[/I]
[I]494*288^18778 + 1 is prime! (a = 5) [46186 digits][/I]

Found with PFGW as a PRP, proved with Proth.exe. (Actually, it was proved first with PFGW...it was found by a script for searching generalized Sieprinski/Riesel conjectures that we use at the Conjectures 'R Us project. The script automatically proves PRPs upon finding them as such, so I didn't have the opportunity to [I]first[/I] prove it with Proth.exe. Does it still count? :smile:)

Edit: sorry, was composing this before you posted your latest requirements for the various categories; scratch #19 and make it #20.

Great. Now that the previous issue has been cleared up.. Post 1000 of the thread! :party:

[QUOTE]Found with PFGW as a PRP, proved with Proth.exe. (Actually, it was proved first with PFGW...it was found by a script for searching generalized Sieprinski/Riesel conjectures that we use at the Conjectures 'R Us project. The script automatically proves PRPs upon finding them as such, so I didn't have the opportunity to first prove it with Proth.exe. Does it still count? :smile:)

Edit: sorry, was composing this before you posted your latest requirements for the various categories; scratch #19 and make it #20.[/QUOTE]

Obsolete tech: No, because the proof was already done by PFGW. You techically used newer tech to do it first. The proof is to be done as follows: Grab the PRP, and have Proth.exe prove it prime. No #20 award for you, but you still get a spot for #2.