lucas lehmer outstretch

[science_man_88]

I was told to post on the forum instead of annoying CRGreathouse. so here I am
basically i wan't to find a way to easily connect certain p values with s in a new way.

s²-2 =k*2^p-1
(s²-2)/k + 1 = 2^p


p=log₂((s²-2)/k + 1)

this works for s(n-1) can we figure out a generalisation for any amount of n change ? if so can we apply it easily and can anyone get the log₂() part reduced more ?

[retina]

Originally Posted by science_man_88

s²-2 =k*2^p-1
(s²-2)/k + 1 = 2^p

Where did you learn your algebra? I'd ask for my money back if I was you.

[CRGreathouse]

There's an arithmetic error in your post.

Originally Posted by science_man_88

this works for s(n-1) can we figure out a generalisation for any amount of n change ? if so can we apply it easily and can anyone get the log₂() part reduced more ?

I don't understand your goal here. What does "for any amount of n change" mean? What does "get the log₂() part reduced more" mean?

[science_man_88]

Originally Posted by CRGreathouse

There's an arithmetic error in your post.



I don't understand your goal here. What does "for any amount of n change" mean? What does "get the log₂() part reduced more" mean?

I can't find the error you talk of, and if it's truly incorrect then why care for either answer.

sorry log₂(2^p)

[science_man_88]

s²-2 =k*(2^p-1) =correction
(s²-2)/k =2^p-1
((s²-2)/k)+1 =2^p
log₂(((s²-2)/k)+1) =p

[science_man_88]

Originally Posted by CRGreathouse

There's an arithmetic error in your post.



I don't understand your goal here. What does "for any amount of n change" mean? What does "get the log₂() part reduced more" mean?

the n change part means for any s within the sequence (so for 2^5-1 instead of using the 5th one in the sequence; n=4 as n=0 for the first; I could try and use a lower number.) the reason a wanted the log₂(((s2-2)/k)+1) reduced is to get a lower comparison of s and p. like p*k isn't that big compared with k*2^p-1 same idea in reducing the log.

[science_man_88]

Originally Posted by science_man_88

the n change part means for any s within the sequence (so for 2^5-1 instead of using the 5th one in the sequence; n=4 as n=0 for the first; I could try and use a lower number.) the reason a wanted the log₂(((s2-2)/k)+1) reduced is to get a lower comparison of s and p. like p*k isn't that big compared with k*2^p-1 same idea in reducing the log.

s=4;*

[science_man_88]

log₂(((s^4 - 4*s^2 + 2)/k)+1) = p is the next one up. I can continue this but the equations get longer and without getting a lower fraction to go with it works out to log(Mersenne number(p) +1) which isn't very helpful.