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An old mathematical puzzle soon to be unraveled?
phys.org ^
| 15 JAN 2014
| Benjamin Augereau
Posted on 01/21/2014 7:34:06 AM PST by onedoug
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To: OldNavyVet
EVERY number is divisible by one, and EVERY even number is divisible by two.
Therefore Prime Numbers must be odd and ... since there is an infinite number of odd numbers, some of which are prime ... it follows that there must be a relatively infinite number of odd prime numbers because infinity is infinity, and infinity is without end.
QED. What about 2? Isn't it prime?
21
posted on
01/21/2014 10:27:53 AM PST
by
OneWingedShark
(Q: Why am I here? A: To do Justly, to love mercy, and to walk humbly with my God.)
To: OneWingedShark
What about 2? Isn't it prime?You're right. Two is a prime number. My thinking was infinitely out of sight.
22
posted on
01/21/2014 10:32:57 AM PST
by
OldNavyVet
(Robert's revenge lies in our getting rid of Democrat control in House, Senate and Preisdent.)
To: zeugma
Do you suppose there might be a finite number of highest numbers?
To: Marylander
Do you suppose there might be a finite number of highest numbers? No, but I have found after running several million tests, that there are major clusters similar to 9232 found in higher regions. One thing that I think is cool is that with the exception of numbers that are powers of 2, (powers of 2 are always the shortest route to 1 for obvious reasons) there is no easy way to guess how many steps a given number will take to get to 1 without running it.
From the list I posted previously...
25 takes 23 steps, and 88 is the highest number reached.
26 takes 10 steps, and 40 is the highest number reached.
27 takes 111 steps, and 9232 is the highest number reached.
28 takes 18 steps, and 52 is the highest number reached.
29 takes 18 steps, and 88 is the highest number reached.
The number 27 is definitely an outlier in the number of required steps.
There are other variations on the Collatz Conjecture. One multiplies by 5 and divides by 2, and has the same result. Strangely that 9232 number pops up there and in other variations as well. I did some searching on the 9232 number and couldn't find anything specific about it.
I wish I'd known about stuff like this when I was young and stupid.
24
posted on
01/21/2014 11:21:25 AM PST
by
zeugma
(Is it evil of me to teach my bird to say "here kitty, kitty"?)
To: zeugma
Kinda bored here, so I thought I'd follow up on the 9232 number. To quantify how often that particular number shows up, lets look at the numbers between 2 and 5000. What percentage of those numbers have 9232 as a part of their 'path' on the Collatz number tree? To find out, I used a bash script that I wrote that will take as input the number to start and stop on. Unfortunately, for my purpose, it also prints out a line that says what the highest number reached was, so we have to suppress it. That's what the "grep -v reached" is for.
$ collatz2 2 5000 | grep 9232 | grep -v reached | wc -l
1996
So out of 5000 numbers, 1996, or 39.9% of them will pass through the number 9232.
Yup. That's a lot. But is it unusual? Well let's take a look at the numbers that surround it...
$ for x in 1 2 3 4 5 6 7 8 9; do
> collatz2 2 5000 | grep 923${x} | grep -v reached | wc -l
> done
0
1996
8
23
0
0
0
2
0
So, looking at the above, that translates to the following
9231 = 0
9232 = 1996
9233 =8
9234 =23
9235 =0
9236 =0
9237 =0
9238 =2
9239 =0
I'd call that unusual. What does it mean, if anything? I have no idea.
25
posted on
01/21/2014 12:12:17 PM PST
by
zeugma
(Is it evil of me to teach my bird to say "here kitty, kitty"?)
To: StayAt HomeMother; Ernest_at_the_Beach; decimon; 1010RD; 21twelve; 24Karet; 2ndDivisionVet; ...
Thanks onedoug.
...the twin primes conjecture... which many science historians have attributed to the Greek mathematician Euclid, deals with prime numbers...
26
posted on
01/21/2014 5:19:19 PM PST
by
SunkenCiv
(;http://www.freerepublic.com/~mestamachine/)
I think the Euclid connection was discovered by Marty McFly when he went back in time from the parking lot of the Twin Primes Mall.
27
posted on
01/21/2014 5:26:47 PM PST
by
SunkenCiv
(;http://www.freerepublic.com/~mestamachine/)
28
posted on
01/21/2014 5:30:56 PM PST
by
SunkenCiv
(;http://www.freerepublic.com/~mestamachine/)
29
posted on
01/21/2014 5:32:00 PM PST
by
SunkenCiv
(;http://www.freerepublic.com/~mestamachine/)
30
posted on
01/21/2014 5:33:33 PM PST
by
SunkenCiv
(;http://www.freerepublic.com/~mestamachine/)
To: onedoug; a fool in paradise; Slings and Arrows
31
posted on
01/21/2014 5:35:16 PM PST
by
Revolting cat!
(Bad things are wrong! Ice cream is delicious! We reserve the right to serve refuse to anyone!)
To: onedoug
The answer is 42.
(HHGTTG)
32
posted on
01/21/2014 6:11:36 PM PST
by
Redcitizen
(Never bring a tank to a Chuck Norris fight.)
To: onedoug
...as I grow older I find myself irresistibly drawn to number theory.I'm much the same. Have you read "Fermat's Enigma"?
I think you'd enjoy it.
33
posted on
01/21/2014 6:56:15 PM PST
by
Straight Vermonter
(Posting from deep behind the Maple Curtain)
To: onedoug
I believe that everything we see as natural laws are manifestations of a single universal Truth. Any conflicts we “see” are due to our inability to be attuned to Him.
34
posted on
01/22/2014 5:25:54 AM PST
by
Pecos
(The Chicago Way: Kill the Constitution, one step at a time.)
To: Straight Vermonter
Read it some years ago.
Yutaka Tanyama was a genius for the ages.
35
posted on
01/22/2014 5:46:04 AM PST
by
onedoug
36
posted on
12/28/2023 10:31:44 AM PST
by
SunkenCiv
(Putin should skip ahead to where he kills himself in the bunker.)
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