Pseudo-mathematical gibberings (volume 9a)

storflyt32 · 2013-11-21, 01:06

Sorry!

Really I should have stuck with the -1 rather than +1 here.

But honestly, +1 probably is the hot subject right now. In the end it is more difficult to be working on and have more unknowns than knowns coming along with it when it comes to possible existing factors.

I am using * for multiplication. Some people prefer the . instead.

Anyway, if I try dividing 2^1968721+1 with 31840750786281 (3*10613583595427), I am left with a number which now has become slightly smaller. Unless proven otherwise, it is assumed to be a composite number where still further numbers (prime numbers getting progressively larger and larger) are thought to be part of this number.

Sieving or factoring is supposed to possibly be able to extract one or more such prime number (or factor) from this larger number. Eventually, the factors remaining (if more than one) becomes so large that it becomes almost impossible to get to them.

In comparison, 2^1048576+1 is thought to be a composite number where no factors apparently are known.

If a factor (possibly a larger one), may exist for someone to find, it may possibly be easier to deduce a composite number before a prime number when trying to divide (or factorize) these numbers with each other, like 50/10 rather than 50/5.

Anyway, sieving is supposed to yield the smaller factors rather than the big ones.

bloodIce · 2013-11-21, 09:49

Most of your conclusions are right. However, did you try to visualize the number you are interested in. Look here: http://factordb.com/index.php?showid...00000634633435 . It is a hard nut to crack. It might take some time to see such numbers fully factored (there are some lucky finds in this range, but generally it is very hard). In the future you may want to consult FactorDB before posting a number here. FactorDB might help you define your problem and show you what is known beforehand.

I do not understand why +1 is hotter than -1, but I guess there is an explanation.

ewmayer · 2013-11-21, 21:33

Quote:

Originally Posted by bloodIce

I do not understand why +1 is hotter than -1, but I guess there is an explanation.

We love them both equally, but appreciate the former's positive attitude.

-1, OTOH is what in German is referred to as a Sorgenkind.

LaurV · 2013-11-22, 00:43

Quote:

Originally Posted by ewmayer

We love them both equally, but appreciate the former's positive attitude.

-1, OTOH is what the in German is referred to as a Sorgenkind.

Which body parts are you talking about?

Brian-E · 2013-11-22, 09:30

Quote:

Originally Posted by LaurV

Which body parts are you talking about?

It means: On Top Of Head.

LaurV · 2013-11-22, 09:44

Well, plus one, minus one, I thought he was talking about bra sizes, but giving the positive attitude, it could also mean condoms...

(what a dirty mind I have)

bloodIce · 2013-11-22, 22:25

I hope those friendly comments are not addressed to me. I still cannot get why 2^n+1 can be cooler than 2^n-1. You would ask why I am so negative, when I say that I prefer "-1"

.

storflyt32 · 2013-11-23, 01:22

Apparently someone was able to conclude that 2^1968721-1 is a composite number as well.

Yes, but anyway, what are the numbers here?

My best guess is that there are no small factors in this number.

Also I am trying out the command
ecm((10344^1024+1)/3243597063038977), using yafu-x64 .

Yes, a new factor apparently having been added there.

Or, alternatively "ecm((10344^1024+1)/3243597063038977)" from the DOS command line in Windows.

3243597063038977=12289*263943124993, by the way.

Apparently, using both the abovementioned command, or the alternative
"ecm((10344^1024+1)/3243597063038977,30)" syntax, based on Yafu, it still apparently crashes out now, both when running directly from Yafu through Windows, or starting up a DOS prompt and fortunately ending up back there. By the way, I only have 8 GB of RAM installed, not 16 GB.

Apparently there is some DOSKEY or the like installed and running, which happens to remember my previous command lines using the up and down arrows on the numerical keypad (NUMLOCK is turned off, by the way).

Should I just push the button for the Microsoft Error Report when it comes to this error problem? The numbers being worked on here are not the biggest ones, but definitely this becomes harder and harder to get at as the smaller factors are being eliminated from the rest of the number(s).

A little edit: Apparently it now takes it, late in the night, in a DOS command prompt window.

Thanks!

Batalov · 2013-11-23, 05:44

Quote:

Originally Posted by bloodIce

I hope those friendly comments are not addressed to me. I still cannot get why 2^n+1 can be cooler than 2^n-1. You would ask why I am so negative, when I say that I prefer "-1"

.

Quote:

Originally Posted by THIS ISLAND EARTH (1954)

He meets through Ruth a Dr. Steve Carlson and a cat named Neutron.
Ruth says, "We call him that because he's so positive."

.

fivemack · 2013-11-23, 08:25

To be slightly serious, I prefer -1 too; because the techniques that prove numbers prime by computing in a multiplicative group don't have scope for handling (2^n+1)/{something small}, and for nearly all n there is an algebraic something-small.

For example, it took quite a lot of work to prove the primality of (2^42737+1)/3 ; (2^83339+1)/3 looks as if it's within the range of possibility for fastECPP using effort comparable to a 175-digit GNFS factorisation.

YuL · 2013-11-23, 14:58

Quote:

Originally Posted by Batalov

Originally Posted by THIS ISLAND EARTH (1954)
He meets through Ruth a Dr. Steve Carlson and a cat named Neutron.
Ruth says, "We call him that because he's so positive."

http://youtu.be/HaK1DPStRUE?t=33s

2013-11-21, 01:06	#1
storflyt32 Feb 2013 2×229 Posts	Pseudo-mathematical gibberings (volume 9a) Sorry! Really I should have stuck with the -1 rather than +1 here. But honestly, +1 probably is the hot subject right now. In the end it is more difficult to be working on and have more unknowns than knowns coming along with it when it comes to possible existing factors. I am using * for multiplication. Some people prefer the . instead. Anyway, if I try dividing 2^1968721+1 with 31840750786281 (310613583595427), I am left with a number which now has become slightly smaller. Unless proven otherwise, it is assumed to be a composite number where still further numbers (prime numbers getting progressively larger and larger) are thought to be part of this number. Sieving or factoring is supposed to possibly be able to extract one or more such prime number (or factor) from this larger number. Eventually, the factors remaining (if more than one) becomes so large that it becomes almost impossible to get to them. In comparison, 2^1048576+1 is thought to be a composite number where no factors apparently are known. If a factor (possibly a larger one), may exist for someone to find, it may possibly be easier to deduce a composite number before a prime number when trying to divide (or factorize) these numbers with each other, like 50/10 rather than 50/5. Anyway, sieving is supposed to yield the smaller factors rather than the big ones. Last fiddled with by storflyt32 on 2013-11-21 at 01:13*

2013-11-21, 09:49	#2
bloodIce Feb 2010 Sweden 173 Posts	FactorDB is your friend Most of your conclusions are right. However, did you try to visualize the number you are interested in. Look here: http://factordb.com/index.php?showid...00000634633435 . It is a hard nut to crack. It might take some time to see such numbers fully factored (there are some lucky finds in this range, but generally it is very hard). In the future you may want to consult FactorDB before posting a number here. FactorDB might help you define your problem and show you what is known beforehand. I do not understand why +1 is hotter than -1, but I guess there is an explanation.

2013-11-22, 22:25	#7
bloodIce Feb 2010 Sweden 173 Posts	Since I have been quoted I hope those friendly comments are not addressed to me. I still cannot get why 2^n+1 can be cooler than 2^n-1. You would ask why I am so negative, when I say that I prefer "-1" .

2013-11-23, 01:22	#8
storflyt32 Feb 2013 2×229 Posts	Apparently someone was able to conclude that 2^1968721-1 is a composite number as well. Yes, but anyway, what are the numbers here? My best guess is that there are no small factors in this number. Also I am trying out the command ecm((10344^1024+1)/3243597063038977), using yafu-x64 . Yes, a new factor apparently having been added there. Or, alternatively "ecm((10344^1024+1)/3243597063038977)" from the DOS command line in Windows. 3243597063038977=12289263943124993, by the way. Apparently, using both the abovementioned command, or the alternative "ecm((10344^1024+1)/3243597063038977,30)" syntax, based on Yafu, it still apparently crashes out now, both when running directly from Yafu through Windows, or starting up a DOS prompt and fortunately ending up back there. By the way, I only have 8 GB of RAM installed, not 16 GB. Apparently there is some DOSKEY or the like installed and running, which happens to remember my previous command lines using the up and down arrows on the numerical keypad (NUMLOCK is turned off, by the way). Should I just push the button for the Microsoft Error Report when it comes to this error problem? The numbers being worked on here are not the biggest ones, but definitely this becomes harder and harder to get at as the smaller factors are being eliminated from the rest of the number(s). A little edit: Apparently it now takes it, late in the night, in a DOS command prompt window. Thanks! Last fiddled with by storflyt32 on 2013-11-23 at 01:42*

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2013-11-22, 09:44	#6
LaurV Romulan Interpreter Jun 2011 Thailand 7×1,373 Posts	Well, plus one, minus one, I thought he was talking about bra sizes, but giving the positive attitude, it could also mean condoms... (what a dirty mind I have)

2013-11-23, 08:25	#10
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 1913₁₆ Posts	To be slightly serious, I prefer -1 too; because the techniques that prove numbers prime by computing in a multiplicative group don't have scope for handling (2^n+1)/{something small}, and for nearly all n there is an algebraic something-small. For example, it took quite a lot of work to prove the primality of (2^42737+1)/3 ; (2^83339+1)/3 looks as if it's within the range of possibility for fastECPP using effort comparable to a 175-digit GNFS factorisation.