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Old 2021-08-28, 15:20   #1
Dobri
 
May 2018

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Post "I am experimenting with heuristic sieves."

21277 - 1 = 1 + 2⋅3⋅5⋅23⋅59⋅89⋅233⋅397⋅683⋅1103⋅1277⋅2089⋅2113⋅18503⋅64439⋅181193⋅3033169⋅107367629⋅...
https://en.wikipedia.org/wiki/Fermat%27s_little_theorem

Last fiddled with by Dobri on 2021-08-28 at 15:36
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Old 2021-08-28, 17:03   #2
Batalov
 
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21277 - 1 = 1 + 2⋅3⋅5⋅23⋅59⋅89⋅233⋅397⋅683⋅1103⋅1277⋅2089⋅2113⋅18503⋅64439⋅181193⋅3033169⋅107367629⋅...
https://en.wikipedia.org/wiki/Fermat%27s_little_theorem
Trolling much?

What does it have to do with anything?
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Old 2021-08-28, 17:50   #3
Dobri
 
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What does it have to do with anything?
I am experimenting with heuristic sieves. One of the heuristics attempts to use the known small factors of 2p-1-1.
Interestingly, in the case of p = 1277, there is a plenty of factors of 2p-1-1.
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Old 2021-08-28, 18:07   #4
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...Interestingly, in the case of p = 1277, there is a plenty of factors of 2p-1-1.
O RLY?
Ever heard of
x2-1 = ... ? (write it out, don't be shy)
x11-1 = ... ? (write it out)

There is so much "interesting" in the world to anyone who skipped all classes in the 7th grade.
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Old 2021-08-28, 18:30   #5
Dobri
 
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There is so much "interesting" in the world to anyone who skipped all classes in the 7th grade.
Obviously, it stems from the observation that 1276 = 4⋅11⋅29. You assume the worst in others.
One should not forget to be polite and respectful to the ones who attempt to communicate instead of posting uncivilized forcible content of provocative and insulting nature as only bullies do from the assumed position of power.
At least, I remember from kindergarten the basics of being kind to people.
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Old 2021-08-28, 19:13   #6
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You assume the worst in others.
You, actually, appear to be assuming the worst in others.

I almost always apply Hanlon's_razor. My remark had nothing to do with you but with your argument.

Do you disagree with an illustrative argument that if a person cut all classes in school in the past, they will later in life find a lot of things interesting and even stunning? "A kilogram of led weighs the same as a kilogram of feathers! Who could have thought?!" You are arguing not with the presented argument, but with the "assumed" fact that it was "about you". It was not.

Whether you immediately project yourself in every sentence is entirely a matter of your choice. Your assumptions.
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Old 2021-08-28, 20:09   #7
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My remark had nothing to do with you but with your argument.
Same here. Only the first line of my previous response was concerned with your comment concerning the homogeneous version of the geometric sum formula.
The rest of said response was an illustrative argument.
As for razors, I do not use such tools. Sometimes, one could inadvertently 'cut' oneself while attempting to apply razors to others.
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Old 2021-08-28, 20:55   #8
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Lightbulb

I can only add another illustrative vignette -

Interestingly (c), 21278-1 is fully factored. But how can that be without the help of factoring 21278-1-1, which is not factored at all beyond the trivial factor of 2? It is one of the two: 1. Wizardry! or 2. Factoring N-1 actually helps nothing to factor N; it is a red herring.
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Old 2021-08-28, 21:17   #9
Dobri
 
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Originally Posted by Batalov View Post
Interestingly (c), 21278-1 is fully factored. But how can that be without the help of factoring 21278-1-1, which is not factored at all beyond the trivial factor of 2? It is one of the two: 1. Wizardry! or 2. Factoring N-1 actually helps nothing to factor N; it is a red herring.
Or 3. The factors could be used indirectly in the design and testing of the heuristic sieve.
Every heuristic initially has an element of wizardry though.
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Old 2021-08-28, 21:50   #10
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Quote:
Originally Posted by Dobri View Post
I am experimenting with heuristic sieves. One of the heuristics attempts to use the known small factors of 2p-1-1.
<snip>
A heuristic is an informed guess. Those offered seriously include the information on which they are based, what simplifying assumptions are being made, and a "plausibility argument" explaining how those principles and assumptions are being applied.

I see no indication that your "heuristic sieve" is informed by anything, or that it is anything other than phantasmagorical. You have provided no motivation for using factors of Mp - 1 in a sieve for trying to factor Mp, and have given absolutely no indication of what set, if any, you might want to use them to sieve.

You are certainly not informed on the subject by what is available on this Forum.

The question of whether factoring Mp - 1 would help in factoring Mp was discussed on this very forum about a year ago, here. It specifically mentions the exponent 1277. And, as of this posting, the thread title is still visible on the Mersenne Forum home page.

The short answer to the question is "No."

I conclude that you have either not bothered to avail yourself of the most basic facts concerning factors of Mp - or are deliberately disregarding them, in which case you are a troll.
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Old 2021-08-28, 23:04   #11
tuckerkao
 
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Quote:
Originally Posted by Batalov View Post
x2-1 = ... ? (write it out, don't be shy)
x11-1 = ... ? (write it out)
x2-1 = (x - 1)(x +1)
x3-1 = (x - 1)(x2 + x + 1)
x3+1 = (x + 1)(x2 - x + 1)

x6-1 = (x3-1)(x3+1)

x11-1 = didn't get any Google Search results, but since there are answers for x5-1 and x5+1, the same patterns should be observable.

x5-1 = (x - 1)(x4 + x3 + x2 + x + 1)
x5+1 = (x + 1)(x4 - x3 + x2 - x + 1)

x2p+1 = Maybe a prime
x2p-1 = Always composite
x2p±1+1 = Always composite
x2p±1-1 = Always composite

Last fiddled with by tuckerkao on 2021-08-29 at 00:03
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