{
	"result":"IMPORTANT: Here are some Wolfram documentation snippets that you should use to respond.

======

<result url='https://reference.wolfram.com/language/ref/GraphData#1002612349'>

# GraphData > Examples > Scope > Detailed 
Properties > Annotatable Properties Related to Graph Output > 18

Return the name of the ordinary line graph of the pentagram configuration:

```wl
In[1]:= GraphData["PentagramConfigurationGraph", "OrdinaryLineGraph", "Name"]

Out[1]= "PetersenGraph"
```

Return the ordinary line graph of the pentagram configuration:

```wl
In[2]:= GraphData["PentagramConfigurationGraph", "OrdinaryLineGraph", "Graph"]

Out[2]= Image[...]
```

Compute by finding the extraordinary lines of the pentagram configuration:

```wl
In[3]:= config = GraphData["PentagramConfigurationGraph", "Graph", "Labeled"]

Out[3]= Image[...]

In[4]:=
v = GraphEmbedding[config];
configurationlines = ResourceFunction["FindExtraordinaryLines"][v]

Out[4]= {}
```

Complement with all possible pairs of points to get the ordinary lines:

```wl
In[5]:= ordinarylines = Complement[Subsets[VertexList[config], 
{2}], Flatten[Subsets[#, {2}]& /@ configurationlines, 1]]

Out[5]= {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 7}, {1, 8}, {1, 9}, {1, 10}, {2, 3}, {2, 4}, 
{2, 5}, {2, 6}, {2, 7}, {2, 8}, {2, 9}, {2, 10}, {3, 4}, {3, 5}, {3, 6}, {3, 7}, {3, 8}, {3,
9}, {3, 10}, {4, 5}, {4, 6}, {4, 7}, {4, 8}, {4, 9}, {4, 10}, {5, 6}, {5, 7}, {5, 8}, {5, 9}, 
{5, 10}, {6, 7}, {6, 8}, {6, 9}, {6, 10}, {7, 8}, {7, 9}, {7, 10}, {8, 9}, {8, 10}, {9, 10}}

In[6]:= connectedpts = Union@Flatten[ordinarylines];
```

Build the ordinary line graph:

```wl
In[7]:= Graph[connectedpts, UndirectedEdge@@@ordinarylines, VertexCoordinates -> v[[connectedpts]]]

Out[7]= Image[...]
```

Identify using ``ToEntity`` :

```wl
In[8]:= ToEntity[%]

Out[8]= Entity["Graph", {"Complete", 10}]
```

</result>

<result url='https://resources.wolframcloud.com/FunctionRepository/resources/TurtleArt#809943932'>

# WFR > TurtleArt > Examples > Neat Examples > Neonsqi

Draw [neonsqi](https://turtleart.org/programming/book1/code.html?6) :

```wl
In[1]:=
Module[{sqi}, 
	sqi[] := Module[{box1 = 0}, 
	ResourceFunction["TurtleArt"]["SetXY"][0, 0];
	ResourceFunction["TurtleArt"]["SetHeading"][0];
	Do[
	ResourceFunction["TurtleArt"]["Forward"][box1];
	ResourceFunction["TurtleArt"]["Right"][89];
	box1 += 10
	, 
	80
	]
	];
	
	ResourceFunction["TurtleArt"]["Clean"][];
	ResourceFunction["TurtleArt"]["SetPensize"][100];
	ResourceFunction["TurtleArt"]["SetColor"][10];
	ResourceFunction["TurtleArt"]["SetShade"][100];
	
	Do[
	sqi[];
	ResourceFunction["TurtleArt"]["SetShade"][ResourceFunction["TurtleArt"]@"Shade" - 8];
	ResourceFunction["TurtleArt"]["SetPensize"][ResourceFunction["TurtleArt"]@"Pensize" - 1]
	, 
	100
	];
	
	ResourceFunction["TurtleArt"]["Draw"][]
	]

Out[1]= !(*GraphicsBox[«7»])
```

</result>

<result url='https://resources.wolframcloud.com/FunctionRepository/resources/DrawSketch#91293614'>

# WFR > DrawSketch > Examples > Neat Examples

Create a function which displays an animation showing the object being drawn from the sequence of pen strokes chosen by the network:

```wl
In[1]:=
animateSketch[obj_] := DynamicModule[{lines, plotRange}, lines = DeleteCases[drawSketch[obj], {}];
	plotRange = Map[MinMax, 1.05 * {lines[[All, All, 1]], lines[[All, All, 2]]}];
	Animate[Graphics[Line@lines[[1 ;; i]], PlotRange -> plotRange], {i, 1, Length[lines], 1}, AnimationRepetitions -> 1]]

In[2]:= animateSketch["Bird"]

Out[2]= Image[...]
```

</result>",
	"code":200,
	"success":true,
	"uuid":"595b6b47-ea8f-4352-af5b-dfcfcf096c17"
}

The following parameters can be passed in the body of an API request:

context (required)

{
 	"context" : [
   		{
    			"role" : "user",
    			"content" : "YOUR PROMPT"
    		},
   		{
    			"role" : "assistant"
      			"content" : "API RESPONSE"
    		},
   		{
    			"role" : "user"
      			"content" : "YOUR NEXT PROMPT"
    		}
   	]
 }

{
	"result":"IMPORTANT: The following information was automatically generated using Wolfram Alpha and should be used to help answer the user's query using factual information.

======

<result query='123456789th prime number' url='https://www.wolframalpha.com/input?i=123456789th+prime+number'>

# Input

p_123456789

# Result

2543568463

# Scientific notation

2.543568463 * 10^9

# Number line

![Number line](https://public6.wolframalpha.com/files/GIF_15vcqcuhd89.gif)

# Number name

2 billion 543 million 568 thousand 463

# Number length

10 decimal digits

# Residues modulo small integers

![Image](https://public6.wolframalpha.com/files/GIF_15vctx718z0.gif)

m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
2543568463 mod m | 1 | 1 | 3 | 3 | 1 | 2 | 7 | 1

# Property

2543568463 is a number that cannot be written as a sum of 3 squares.

2543568463 is the 123456789th prime number.

2543568463 is an odd number.

# Density of primes <= 2543568463

0.0485368

# Comparison

≈ 0.32 × the number of people alive today (≈ 7.8×10^9)

# Series representation

p_123456789 = 2 + sum_(k=2)^floor(2 + 246913578 log(123456789))(1 - floor(π(k)/123456789))

p_123456789 = 1 + sum_(k=1)^(2^123456789) 
floor(3^(2/123456789) 13717421^(1/123456789) (1/(1 + π(k)))^(1/123456789))

p_123456789 = sum_(k=0)^15241578750190521 g(1 - g(-123456789 + sum_(j=0)^k r((g(-1 
+ j)!)^2, j))) for (g(m) = m θ(m) and δ_(0, b) (a - a mod b) + a mod b = r(a, b))

# Neighboring primes

p_123456788 = 2543568457 | p_123456790 = 2543568479

</result>

======

You can use any Markdown links from these results in your response to show images, formatted expressions, etc. to the user.

If you use any information from these results, you should cite the relevant URL with a Markdown link in your response.",
	"code":200,
	"success":true,
	"uuid":"6b56b1f3-c274-4de4-a142-e5f31991c279"
}

count (optional)