﻿ A Math... Question :)
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Xeda112358
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 « on: 17 September, 2011, 17:56:49 » 0

I have a little math challenge for y'all… This one isn't difficult so long as you don't overthink it, but if you do (like me) you will probably laugh at the simple solution. My hope is that you are like me and this keeps you occupied for a little while :

Find 132 consecutive composite natural numbers.

• Natural numbers are {1,2,3,4,…}
• A composite number is a number that isn't prime like 15 (15=3*5)
• An example of 12 consecutive composites is: {114,115,116,117,…,125,126}

I have two solutions that I came up with (one of them required Latex)
Have fun!?
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Chromatic polynomials
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sqrt(Time)
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 « Reply #1 on: 17 September, 2011, 19:20:21 » 0

I got an answer almost instantly, but that's just because I've seen this exact kind of problem done before. ^_^ (I guess that's cheating)
It is indeed fun...
I'm wondering what your second solution is?
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 « Reply #2 on: 17 September, 2011, 19:38:42 » 0

Here:
-132 through 0
Its too easy

P.S. I did overthink it. I looked of a list with 50 million prime numbers and couldn't find such a gap.

EDIT: Oh wait... those aren't natural...
 « Last Edit: 17 September, 2011, 19:42:23 by boot2490 » Logged

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 « Reply #3 on: 17 September, 2011, 19:41:42 » 0

Is that a negative 132?
• Natural numbers are {1,2,3,4,…}
Also, such a gap does indeed exist In fact, there exists much more massive gaps

EDIT: Also, sqrt(Time), if you want to pm me your solution, feel free or you can wait until others have found it
 « Last Edit: 17 September, 2011, 19:44:06 by Xeda112358 » Logged

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My pastebin
Spoiler for FileSyst:
FileSyst is an application that provides a folder and filesystem for the TI-83+/84+ calculators. It is designed to be easy to access and use in BASIC, and it can be used to access game files and save data, or to create a command prompt, among other things:

Spoiler for Graphiti:
This is a graph explorer for graph theory. It will require lots of work to finish. Currently you can:
Add edges (direction not shown, but they are directed)
Arrange vertices in a circle (in the future, you will be able to define levels of rings and the number of nodes in each)
Create complete graphs quickly

Plans:
Deleting edges
Multiple graphs support
Arrows for directed graphs
Planarity testing
Matrix operations
Weighted edges
Chromatic polynomials
Chromatic numbers

Spoiler for Stats:

Samocal             [o---------]
Virtual Processor   [o---------]
EnG                 [oo--------]
Grammer             [ooo-------]
AsmComp             [ooo-------]
Partex              [oooo------]
BatLib              [oooooooo--]
Grammer82           [----------]
Grammer68000        [----------]

Pseudonyms:  Zeda, Xeda, Thunderbolt
Languages:   English, français
Programming: z80 Assmebly
Grammer
TI-BASIC (83/84/+/SE, 89/89t/92)
Known For:   -Creator of the Grammer programming language
(Winning program of zContest2011)
-BatLib- One of the most feature packed libraries for BASIC programmers available
with over 100 functions and a simple programming language
-Learning to program z80 in hexadecimal before using an assembler (no computer was
available!)
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 « Reply #4 on: 17 September, 2011, 19:44:29 » 0

Hmm, I'll be interested to see a solution.  I've never seen this problem before, so I don't know the solution or a way to obtain it; hence, I've been playing around with some ideas in GHCi, to no current avail.
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 « Reply #5 on: 17 September, 2011, 19:49:45 » 0

Yeah,
m39 through that plus 132.
Primes.zip has a text file in it with all of the digits. It is over 4 megabytes.
Whoa.
 primes.zip (2264.49 KB - downloaded 27 times.) « Last Edit: 17 September, 2011, 19:57:03 by boot2490 » Logged

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 « Reply #6 on: 17 September, 2011, 19:50:23 » 0

is that a mersenne prime (out of curiosity)?
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Spoiler for FileSyst:
FileSyst is an application that provides a folder and filesystem for the TI-83+/84+ calculators. It is designed to be easy to access and use in BASIC, and it can be used to access game files and save data, or to create a command prompt, among other things:

Spoiler for Graphiti:
This is a graph explorer for graph theory. It will require lots of work to finish. Currently you can:
Add edges (direction not shown, but they are directed)
Arrange vertices in a circle (in the future, you will be able to define levels of rings and the number of nodes in each)
Create complete graphs quickly

Plans:
Deleting edges
Multiple graphs support
Arrows for directed graphs
Planarity testing
Matrix operations
Weighted edges
Chromatic polynomials
Chromatic numbers

Spoiler for Stats:

Samocal             [o---------]
Virtual Processor   [o---------]
EnG                 [oo--------]
Grammer             [ooo-------]
AsmComp             [ooo-------]
Partex              [oooo------]
BatLib              [oooooooo--]
Grammer82           [----------]
Grammer68000        [----------]

Pseudonyms:  Zeda, Xeda, Thunderbolt
Languages:   English, français
Programming: z80 Assmebly
Grammer
TI-BASIC (83/84/+/SE, 89/89t/92)
Known For:   -Creator of the Grammer programming language
(Winning program of zContest2011)
-BatLib- One of the most feature packed libraries for BASIC programmers available
with over 100 functions and a simple programming language
-Learning to program z80 in hexadecimal before using an assembler (no computer was
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 « Reply #7 on: 17 September, 2011, 19:57:40 » 0

Si senor.
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 « Reply #8 on: 17 September, 2011, 19:59:54 » 0

Okay, well I do not have the computational power to test those values, but if you can show me that the next prime is greater than 133 digits away, I will accept that Note that if you are comparing, say, m34 to m35, that does not say that the next prime after m34 is m35 It just says that is the next mersenne prime
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FileSyst is an application that provides a folder and filesystem for the TI-83+/84+ calculators. It is designed to be easy to access and use in BASIC, and it can be used to access game files and save data, or to create a command prompt, among other things:

Spoiler for Graphiti:
This is a graph explorer for graph theory. It will require lots of work to finish. Currently you can:
Add edges (direction not shown, but they are directed)
Arrange vertices in a circle (in the future, you will be able to define levels of rings and the number of nodes in each)
Create complete graphs quickly

Plans:
Deleting edges
Multiple graphs support
Arrows for directed graphs
Planarity testing
Matrix operations
Weighted edges
Chromatic polynomials
Chromatic numbers

Spoiler for Stats:

Samocal             [o---------]
Virtual Processor   [o---------]
EnG                 [oo--------]
Grammer             [ooo-------]
AsmComp             [ooo-------]
Partex              [oooo------]
BatLib              [oooooooo--]
Grammer82           [----------]
Grammer68000        [----------]

Pseudonyms:  Zeda, Xeda, Thunderbolt
Languages:   English, français
Programming: z80 Assmebly
Grammer
TI-BASIC (83/84/+/SE, 89/89t/92)
Known For:   -Creator of the Grammer programming language
(Winning program of zContest2011)
-BatLib- One of the most feature packed libraries for BASIC programmers available
with over 100 functions and a simple programming language
-Learning to program z80 in hexadecimal before using an assembler (no computer was
available!)
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 « Reply #9 on: 18 September, 2011, 01:51:03 » 0

m39 is THE LARGEST prime number known to man. If the next one was less than 133 away, we would have found it by now.

P.S. How is my sig? suggestions?
 « Last Edit: 18 September, 2011, 01:51:35 by boot2490 » Logged

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 « Reply #10 on: 18 September, 2011, 01:55:34 » 0

Actually, that is not true That might be the largest known prime (I think there are a few larger ones that have been found), but there is a special algorithm for testing mersenne primes. This method couldn't be applied to the 134 values after it

(this is why not all of the values between mersenne primes have been tested)
 « Last Edit: 18 September, 2011, 01:57:18 by Xeda112358 » Logged

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My pastebin
Spoiler for FileSyst:
FileSyst is an application that provides a folder and filesystem for the TI-83+/84+ calculators. It is designed to be easy to access and use in BASIC, and it can be used to access game files and save data, or to create a command prompt, among other things:

Spoiler for Graphiti:
This is a graph explorer for graph theory. It will require lots of work to finish. Currently you can:
Add edges (direction not shown, but they are directed)
Arrange vertices in a circle (in the future, you will be able to define levels of rings and the number of nodes in each)
Create complete graphs quickly

Plans:
Deleting edges
Multiple graphs support
Arrows for directed graphs
Planarity testing
Matrix operations
Weighted edges
Chromatic polynomials
Chromatic numbers

Spoiler for Stats:

Samocal             [o---------]
Virtual Processor   [o---------]
EnG                 [oo--------]
Grammer             [ooo-------]
AsmComp             [ooo-------]
Partex              [oooo------]
BatLib              [oooooooo--]
Grammer82           [----------]
Grammer68000        [----------]

Pseudonyms:  Zeda, Xeda, Thunderbolt
Languages:   English, français
Programming: z80 Assmebly
Grammer
TI-BASIC (83/84/+/SE, 89/89t/92)
Known For:   -Creator of the Grammer programming language
(Winning program of zContest2011)
-BatLib- One of the most feature packed libraries for BASIC programmers available
with over 100 functions and a simple programming language
-Learning to program z80 in hexadecimal before using an assembler (no computer was
available!)
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 « Reply #11 on: 18 September, 2011, 02:00:34 » 0

I see. So there are likely those higher but not mersenne.
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 « Reply #12 on: 18 September, 2011, 02:00:45 » 0

Pretty easy. I got it!
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Xeda112358
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 « Reply #13 on: 18 September, 2011, 02:03:31 » 0

Well, I present you two answers...
Actually, only 1 since it was posted in IRC I will tell the other to Qwerty.55 if he wants, but I leave it up to you guys to find the other method

Theorem: If n and k are natural numbers where n is less than or equal to k, n|(k!+n)
Proof:
Let k and n be natural numbers
Since n is less than or equal to k, n is a factor of k!, so n|k!
Therefore, n|(k!+n)

A corollary follows that {k!+2,k!+3,k!+4,...,k!+k} is a sequence of k-1 composite numbers

So, if k=133, we have a sequence of at least 132 composite numbers
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Spoiler for FileSyst:
FileSyst is an application that provides a folder and filesystem for the TI-83+/84+ calculators. It is designed to be easy to access and use in BASIC, and it can be used to access game files and save data, or to create a command prompt, among other things:

Spoiler for Graphiti:
This is a graph explorer for graph theory. It will require lots of work to finish. Currently you can:
Add edges (direction not shown, but they are directed)
Arrange vertices in a circle (in the future, you will be able to define levels of rings and the number of nodes in each)
Create complete graphs quickly

Plans:
Deleting edges
Multiple graphs support
Arrows for directed graphs
Planarity testing
Matrix operations
Weighted edges
Chromatic polynomials
Chromatic numbers

Spoiler for Stats:

Samocal             [o---------]
Virtual Processor   [o---------]
EnG                 [oo--------]
Grammer             [ooo-------]
AsmComp             [ooo-------]
Partex              [oooo------]
BatLib              [oooooooo--]
Grammer82           [----------]
Grammer68000        [----------]

Pseudonyms:  Zeda, Xeda, Thunderbolt
Languages:   English, français
Programming: z80 Assmebly
Grammer
TI-BASIC (83/84/+/SE, 89/89t/92)
Known For:   -Creator of the Grammer programming language
(Winning program of zContest2011)
-BatLib- One of the most feature packed libraries for BASIC programmers available
with over 100 functions and a simple programming language
-Learning to program z80 in hexadecimal before using an assembler (no computer was
available!)
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 « Reply #14 on: 18 September, 2011, 04:24:02 » 0

my solution was 10^120000 to 10^120000+132. (I wrote a prog in python to test that, since I was pretty sure there weren't many primes up there)
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