So what are the possible drivers we can gain? and under what circumstances?

[QUOTE=flagrantflowers;448112]So what are the possible drivers we can gain? and under what circumstances?[/QUOTE]
The downdriver is a class 1 driver, meaning the total powers of 2 in sigma(odd part) cannot exceed 1.

Given that the odd part has at least two factors, and that sigma(prime) is even and there's at least two such primes, the total powers of sigma(C) in 2*C is at least 2 (and we can go a bit further, since C is 3 mod 4, we can in fact say that there's at least three powers of 2 in the sigma of the primes in C).

So no mutation. Only 2 * P (* Q^2) where P is 1 mod 4 will result in a mutation (any even powers of primes don't count, so when I say "only 2*p" I mean after ignoring perfect squares).

To be clear, we are talking about index 10796 which is 2*C185 (otherwise this talk will have no relevance after few more terms are added, nobody will know what we were talking about). Splitting C185 in 2 (or more) primes will not change the downdriver, as Dubslow said. Except of course when the split is p*q^2 with p prime and 1 (mod 4), and q a product of one or more primes, which is very unlikely at this point. We "need" the term to be a 2 multiplied by a [U]single[/U] prime (squares ignored) to have a 50% "chance" to lose the downdriver. I use quotes because we don't actually "need" that :razz:, and the "chance" in that case will be misfortune... hehe...

[QUOTE=LaurV;448122]I use quotes because we don't actually "need" that :razz:, and the "chance" in that case will be misfortune... hehe...[/QUOTE]

Also called the [I][B]risk[/B][/I]. It seems that the word "risk" is not used very often? At least I often see "chance" being used to describe something negative, and it looks wrong to me, and I'm thinking: "Are they really hoping for that outcome?". I guess I was brought up using "risk" so it comes natural.

[QUOTE=LaurV;448122]To be clear, we are talking about index 10796 which is 2*C185 (otherwise this talk will have no relevance after few more terms are added, nobody will know what we were talking about). Splitting C185 in 2 (or more) primes will not change the downdriver, as Dubslow said. Except of course when the split is p*q^2 with p prime and 1 (mod 4), and q a product of one or more primes, which is very unlikely at this point.[/QUOTE]

This C185 has survived a lot of ECM at this point, so I think the likelihood of it having more than 2 factors is pretty low.

GNFS starting now...

[offtopic]

[QUOTE=ATH;448144]Also called the [I][B]risk[/B][/I]. It seems that the word "risk" is not used very often? At least I often see "chance" being used to describe something negative, and it looks wrong to me, and I'm thinking: "Are they really hoping for that outcome?". I guess I was brought up using "risk" so it comes natural.[/QUOTE]

We didn't know we can use "risk" in this context. We learn something new everyday. For us, risk is the money we lose when we trade Forex... :smile:
For us, "chance" is a percent or a number between 0 and 1. We were never thinking to "risk" as a percent or under-unit number (like in probabilities). We see "risk factor" as possibility (unquantifiable) not as a probability (numbers). Even now after your comment, we are tempted to say "the chance of risk".

OTOH, we guessed somehow that a word for "negative chance" or "chance of jinxing it" must exist in English, only we didn't know the word. Thanks for the info...

[/offtopic]

Consider "the risk of failure" versus "the chance of success". Risk can be used in much the same way, i.e. as a probability between 0 and 1.

"Chance of risk" would be seen as redundant -- not a phrase a native speaker would use (at least not in my experience; languages, especially English, have a certain way of contradicting any firm statement one might make about them).

[CODE]Mon Dec 5 03:10:41 2016 p84 factor: 185596989654008443816154517215981298046822949687813530269384349965625218099819665917
Mon Dec 5 03:10:41 2016 p102 factor: 144103322597284487319028362827830047182446040144943320906819406487398249398651395159960993902986495231[/CODE]

Below 180 digits.

Oh noes!

There's still hope ...