Guess the Function for Scatterplot of Number Theoretic Function
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To my knowledge, this puzzle is not previously published (except by me on google+ recently), but I would be interested to hear of any info otherwise.
This following graph was generated using a simple ruby program and gnuplot. It graphs a "basic/fundamental" number theoretic property of the natural numbers. Can you figure out what it is? Increasingly detailed hints below if you want more help. The answer and further background will be posted as a comment after some time.
hint1:
"fundamental" as in "fundamental theorem of arithmetic"
hint2:
one word: prime
hint3:
prime decomposition
mathematics pattern
asked Aug 8 '14 at 20:23
vznvzn
1134
$endgroup$
add a comment |
$begingroup$
To my knowledge, this puzzle is not previously published (except by me on google+ recently), but I would be interested to hear of any info otherwise.
This following graph was generated using a simple ruby program and gnuplot. It graphs a "basic/fundamental" number theoretic property of the natural numbers. Can you figure out what it is? Increasingly detailed hints below if you want more help. The answer and further background will be posted as a comment after some time.
hint1:
"fundamental" as in "fundamental theorem of arithmetic"
hint2:
one word: prime
hint3:
prime decomposition
mathematics pattern
asked Aug 8 '14 at 20:23
vznvzn
1134
$endgroup$
$begingroup$
What does mean "graphs a "basic fundamental" number theoretic property of the natural numbers"? Can you give an example how you graph a property of numbers?
$endgroup$
– klm123
Aug 8 '14 at 20:30
$begingroup$
let x be a natural number and y=f(x) be some simple number-theoretic function of x.
$endgroup$
– vzn
Aug 8 '14 at 20:37
$begingroup$
and what then? How do you graph it? take all possible natural numbers X and put (y,x) points on the graph?
$endgroup$
– klm123
Aug 8 '14 at 20:50
$begingroup$
as axis labels on graph state x ∈ [1..1000]
$endgroup$
– vzn
Aug 8 '14 at 21:09
add a comment |
$begingroup$
To my knowledge, this puzzle is not previously published (except by me on google+ recently), but I would be interested to hear of any info otherwise.
This following graph was generated using a simple ruby program and gnuplot. It graphs a "basic/fundamental" number theoretic property of the natural numbers. Can you figure out what it is? Increasingly detailed hints below if you want more help. The answer and further background will be posted as a comment after some time.
hint1:
"fundamental" as in "fundamental theorem of arithmetic"
hint2:
one word: prime
hint3:
prime decomposition
mathematics pattern
asked Aug 8 '14 at 20:23
vznvzn
1134
$endgroup$
To my knowledge, this puzzle is not previously published (except by me on google+ recently), but I would be interested to hear of any info otherwise.
This following graph was generated using a simple ruby program and gnuplot. It graphs a "basic/fundamental" number theoretic property of the natural numbers. Can you figure out what it is? Increasingly detailed hints below if you want more help. The answer and further background will be posted as a comment after some time.
hint1:
"fundamental" as in "fundamental theorem of arithmetic"
hint2:
one word: prime
hint3:
prime decomposition
mathematics pattern
mathematics pattern
asked Aug 8 '14 at 20:23
vznvzn
1134
asked Aug 8 '14 at 20:23
vznvzn
1134
edited Dec 13 '17 at 17:22
user31569
asked Aug 8 '14 at 20:23
vznvzn
1134
asked Aug 8 '14 at 20:23
vznvzn
1134
asked Aug 8 '14 at 20:23
vznvzn
1134
1134
$begingroup$
What does mean "graphs a "basic fundamental" number theoretic property of the natural numbers"? Can you give an example how you graph a property of numbers?
$endgroup$
– klm123
Aug 8 '14 at 20:30
$begingroup$
let x be a natural number and y=f(x) be some simple number-theoretic function of x.
$endgroup$
– vzn
Aug 8 '14 at 20:37
$begingroup$
and what then? How do you graph it? take all possible natural numbers X and put (y,x) points on the graph?
$endgroup$
– klm123
Aug 8 '14 at 20:50
$begingroup$
as axis labels on graph state x ∈ [1..1000]
$endgroup$
– vzn
Aug 8 '14 at 21:09
add a comment |
$begingroup$
What does mean "graphs a "basic fundamental" number theoretic property of the natural numbers"? Can you give an example how you graph a property of numbers?
$endgroup$
– klm123
Aug 8 '14 at 20:30
$begingroup$
let x be a natural number and y=f(x) be some simple number-theoretic function of x.
$endgroup$
– vzn
Aug 8 '14 at 20:37
$begingroup$
and what then? How do you graph it? take all possible natural numbers X and put (y,x) points on the graph?
$endgroup$
– klm123
Aug 8 '14 at 20:50
$begingroup$
as axis labels on graph state x ∈ [1..1000]
$endgroup$
– vzn
Aug 8 '14 at 21:09
$begingroup$
What does mean "graphs a "basic fundamental" number theoretic property of the natural numbers"? Can you give an example how you graph a property of numbers?
$endgroup$
– klm123
Aug 8 '14 at 20:30
$begingroup$
What does mean "graphs a "basic fundamental" number theoretic property of the natural numbers"? Can you give an example how you graph a property of numbers?
$endgroup$
– klm123
Aug 8 '14 at 20:30
$begingroup$
let x be a natural number and y=f(x) be some simple number-theoretic function of x.
$endgroup$
– vzn
Aug 8 '14 at 20:37
$begingroup$
let x be a natural number and y=f(x) be some simple number-theoretic function of x.
$endgroup$
– vzn
Aug 8 '14 at 20:37
$begingroup$
and what then? How do you graph it? take all possible natural numbers X and put (y,x) points on the graph?
$endgroup$
– klm123
Aug 8 '14 at 20:50
$begingroup$
and what then? How do you graph it? take all possible natural numbers X and put (y,x) points on the graph?
$endgroup$
– klm123
Aug 8 '14 at 20:50
$begingroup$
as axis labels on graph state x ∈ [1..1000]
$endgroup$
– vzn
Aug 8 '14 at 21:09
$begingroup$
as axis labels on graph state x ∈ [1..1000]
$endgroup$
– vzn
Aug 8 '14 at 21:09
add a comment |
2 Answers
2
active
oldest
votes
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This would appear to be a plot of
$x$ against its largest prime factor. The points on the top line are primes, the next line down are primes times two, then primes times three, and so on, with the scattering at the bottom being as a result of numbers that are a product of more than two primes.
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
$endgroup$
$begingroup$
That was my thought too.
$endgroup$
– Kevin
Aug 8 '14 at 23:03
$begingroup$
yep! thx for playing! see also mining number theory for analogies for the ruby code or for further angles/ bkg/ discussion drop by math elementary number theory chat
$endgroup$
– vzn
Aug 8 '14 at 23:12
add a comment |
$begingroup$
ratio of prime number to its preceding gap
answered 7 mins ago
Grant HughesGrant Hughes
1
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
This would appear to be a plot of
$x$ against its largest prime factor. The points on the top line are primes, the next line down are primes times two, then primes times three, and so on, with the scattering at the bottom being as a result of numbers that are a product of more than two primes.
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
$endgroup$
$begingroup$
That was my thought too.
$endgroup$
– Kevin
Aug 8 '14 at 23:03
$begingroup$
yep! thx for playing! see also mining number theory for analogies for the ruby code or for further angles/ bkg/ discussion drop by math elementary number theory chat
$endgroup$
– vzn
Aug 8 '14 at 23:12
add a comment |
$begingroup$
This would appear to be a plot of
$x$ against its largest prime factor. The points on the top line are primes, the next line down are primes times two, then primes times three, and so on, with the scattering at the bottom being as a result of numbers that are a product of more than two primes.
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
$endgroup$
$begingroup$
That was my thought too.
$endgroup$
– Kevin
Aug 8 '14 at 23:03
$begingroup$
yep! thx for playing! see also mining number theory for analogies for the ruby code or for further angles/ bkg/ discussion drop by math elementary number theory chat
$endgroup$
– vzn
Aug 8 '14 at 23:12
add a comment |
$begingroup$
This would appear to be a plot of
$x$ against its largest prime factor. The points on the top line are primes, the next line down are primes times two, then primes times three, and so on, with the scattering at the bottom being as a result of numbers that are a product of more than two primes.
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
$endgroup$
This would appear to be a plot of
$x$ against its largest prime factor. The points on the top line are primes, the next line down are primes times two, then primes times three, and so on, with the scattering at the bottom being as a result of numbers that are a product of more than two primes.
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
edited Aug 8 '14 at 23:04
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
answered Aug 8 '14 at 22:56
qaphlaqaphla
37616
37616
$begingroup$
That was my thought too.
$endgroup$
– Kevin
Aug 8 '14 at 23:03
$begingroup$
yep! thx for playing! see also mining number theory for analogies for the ruby code or for further angles/ bkg/ discussion drop by math elementary number theory chat
$endgroup$
– vzn
Aug 8 '14 at 23:12
add a comment |
$begingroup$
That was my thought too.
$endgroup$
– Kevin
Aug 8 '14 at 23:03
$begingroup$
yep! thx for playing! see also mining number theory for analogies for the ruby code or for further angles/ bkg/ discussion drop by math elementary number theory chat
$endgroup$
– vzn
Aug 8 '14 at 23:12
$begingroup$
That was my thought too.
$endgroup$
– Kevin
Aug 8 '14 at 23:03
$begingroup$
That was my thought too.
$endgroup$
– Kevin
Aug 8 '14 at 23:03
$begingroup$
yep! thx for playing! see also mining number theory for analogies for the ruby code or for further angles/ bkg/ discussion drop by math elementary number theory chat
$endgroup$
– vzn
Aug 8 '14 at 23:12
$begingroup$
yep! thx for playing! see also mining number theory for analogies for the ruby code or for further angles/ bkg/ discussion drop by math elementary number theory chat
$endgroup$
– vzn
Aug 8 '14 at 23:12
add a comment |
$begingroup$
ratio of prime number to its preceding gap
answered 7 mins ago
Grant HughesGrant Hughes
1
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
ratio of prime number to its preceding gap
answered 7 mins ago
Grant HughesGrant Hughes
1
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
ratio of prime number to its preceding gap
answered 7 mins ago
Grant HughesGrant Hughes
1
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
ratio of prime number to its preceding gap
answered 7 mins ago
Grant HughesGrant Hughes
1
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 7 mins ago
Grant HughesGrant Hughes
1
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 7 mins ago
Grant HughesGrant Hughes
1
answered 7 mins ago
Grant HughesGrant Hughes
1
1
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Grant Hughes is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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$begingroup$
What does mean "graphs a "basic fundamental" number theoretic property of the natural numbers"? Can you give an example how you graph a property of numbers?
$endgroup$
– klm123
Aug 8 '14 at 20:30
$begingroup$
let x be a natural number and y=f(x) be some simple number-theoretic function of x.
$endgroup$
– vzn
Aug 8 '14 at 20:37
$begingroup$
and what then? How do you graph it? take all possible natural numbers X and put (y,x) points on the graph?
$endgroup$
– klm123
Aug 8 '14 at 20:50
$begingroup$
as axis labels on graph state x ∈ [1..1000]
$endgroup$
– vzn
Aug 8 '14 at 21:09