Final Lucas Lehmer residuals and Pythagorean triples

[chalsall]

Originally Posted by xilman

Hardly anything which is trivial is also worth pointing out. Indeed, that could serve as a definition of "trivial".

I have learnt the hard way that sometimes language is a barrier.

The use of the word "nominal", for example.

[a nicol]

Originally Posted by Batalov

You don't.*

The method is: run Prime95 with the OutputIterations (iirc) changed...
If you want the same for s₀ = 10, set InitialLLValue=10 in prime.txt.
If you want the same for s₀ = 2/3, set InitialLLValue=23 in prime.txt

Just go and read there -
http://mersenneforum.org/showpost.ph...9&postcount=30

____
* Google for "Now that you've found it, it's gone / Now that you feel it, you don't".
No, there is no hidden meaning in this footnote. Most of the time, the point of that poem is true - for everyone.

There's only one method?

[science_man_88]

Originally Posted by a nicol

Why, mathematically speaking, do these signs vary depending on the start value? Seems like there's a very large dense class theoretical answer to that. Maybe someone could help simplify the answer with some kind of visual analogy?

it's how they are defined in that paper. or that's the simple answer. maybe it has to do with the difference at that point in the test being a specific remainder mod another value we don't know ( or at least I don't).

[a nicol]

Originally Posted by science_man_88

it's how they are defined in that paper. or that's the simple answer. maybe it has to do with the difference at that point in the test being a specific remainder mod another value we don't know ( or at least I don't).

Maybe the answer will become apparent to someone in some small part via referencing integer sequences. Certainly the many thousands of published papers that reference the OEIS as a data point think this is a worthwhile approach to novel mathematical research. Not some here, apparently.

[science_man_88]

Originally Posted by a nicol

Maybe the answer will become apparent to someone in some small part via referencing integer sequences. Certainly the many thousands of published papers that reference the OEIS as a data point think this is a worthwhile approach to novel mathematical research. Not some here, apparently.

I think they are just trying to be more rigorous, than randomly guessing. theory on Mersenne primes ? might be a nice thread for you to read for light reading. you can do other versions of LL as well it's just not really helpful computationally.

[a nicol]

Originally Posted by science_man_88

I think they are just trying to be more rigorous, than randomly guessing. theory on Mersenne primes ? might be a nice thread for you to read for light reading. you can do other versions of LL as well it's just not really helpful computationally.

Cataloguing novel sequences and coincidental connections is a valid research approach period imo. That is the whole premise of the OEIS.

[chalsall]

Originally Posted by science_man_88

I think they are just trying to be more rigorous, than randomly guessing.

A sincere question SM88: Why do you seem so very comfortable just guessing?

[science_man_88]

Originally Posted by a nicol

Cataloguing novel sequences and coincidental connections is a valid research approach period imo. That is the whole premise of the OEIS.

there are infinitely many starting values for the LL test in it's different forms.

https://oeis.org/A018844 ( the minimal start values using the usualy square and subtract 2 method.)

https://oeis.org/A084765 without the starting 1 just one of infinitely many sequences using the square times 2 and then minus 1 version.

[science_man_88]

Originally Posted by chalsall

A sincere question SM88: Why do you seem so very comfortable just guessing?

because that's how most sciences work ( not math sadly) you start out with a hunch show it's implications ( something I fail at doing) and see if it's sturdy.

[a nicol]

Originally Posted by Batalov

You don't.*

The method is: run Prime95 with the OutputIterations (iirc) changed...
If you want the same for s₀ = 10, set InitialLLValue=10 in prime.txt.
If you want the same for s₀ = 2/3, set InitialLLValue=23 in prime.txt

Just go and read there -
http://mersenneforum.org/showpost.ph...9&postcount=30

Thank you, I wasn't aware that table existed (hard to search for).

If S[0]=4 is 14,194,37634.. What is the sequence for S[0]=2/3?

[science_man_88]

Originally Posted by a nicol

Thank you, I wasn't aware that table existed (hard to search for).

If S[0]=4 is 14,194,37634.. What is the sequence for S[0]=2/3?

how is 2/3 defined in a modular ring ... that will give you your answer.