Goldbach's comet: Difference between revisions
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=={{header|ALGOL 68}}== |
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Generates an ASCII-Art scatter plot - the vertical axis is n/10 and the hotizontal is G(n). |
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{{libheader|ALGOL 68-primes}} |
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<lang algol68>BEGIN # calculate values of the Goldbach function G where G(n) is the number # |
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# of prime pairs that sum to n, n even and > 2 # |
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# generates an ASCII scatter plot of G(n) up to G(2000) # |
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PR read "primes.incl.a68" PR # include prime utilities # |
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INT max number = 1 000 000; # maximum number we will consider # |
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# get a list of primes up to max number # |
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[]INT prime list = EXTRACTPRIMESUPTO max number FROMPRIMESIEVE PRIMESIEVE max number; |
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[ 1 : max number ]INT g2; # table of G values: g2[n] = G(2n) # |
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# construct the table of G values # |
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FOR n TO UPB g2 DO g2[ n ] := 0 OD; |
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g2[ 2 ] := 1; # 4 is the only sum of two even primes # |
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FOR n FROM 2 TO UPB prime list DO |
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INT p = prime list[ n ]; |
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g2[ p ] +:= 1; |
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FOR m FROM n + 1 TO UPB prime list |
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WHILE INT sum = p + prime list[ m ]; |
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sum <= max number |
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DO |
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g2[ sum OVER 2 ] +:= 1 |
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OD |
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OD; |
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# show the first hundred G values # |
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FOR n FROM 2 TO 101 DO |
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print( ( whole( g2[ n ], -4 ) ) ); |
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IF ( n - 1 ) MOD 10 = 0 THEN print( ( newline ) ) FI |
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OD; |
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# G( 1 000 000 ) # |
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print( ( "G(", whole( max number, 0 ), "): " |
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, whole( g2[ max number OVER 2 ], 0 ) |
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, newline |
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) |
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); |
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# find the maximum value of G up to the maximum plot size # |
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INT max plot = 2000; |
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INT max g := 0; |
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FOR n TO max plot OVER 2 DO |
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IF g2[ n ] > max g THEN max g := g2[ n ] FI |
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OD; |
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# draw an ASCII scatter plot of G, each position represents 10 G values # |
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# the vertical axis is n, the horizontal axis is G(n) # |
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INT plot step = 10; |
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STRING plot value = " .-+=*%$&#@"; |
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FOR g BY plot step TO ( max plot OVER 2 ) - plot step DO |
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[ 0 : max g ]INT values; |
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FOR v pos FROM LWB values TO UPB values DO values[ v pos ] := 0 OD; |
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INT max v := 0; |
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FOR g element FROM g TO g + ( plot step - 1 ) DO |
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INT g2 value = g2[ g element ]; |
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values[ g2 value ] +:= 1; |
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IF g2 value > max v THEN max v := g2 value FI |
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OD; |
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print( ( IF g MOD 100 = 1 THEN "+" ELSE "|" FI ) ); |
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FOR v pos FROM LWB values TO max v DO |
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print( ( plot value[ values[ v pos ] + 1 ] ) ) |
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OD; |
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print( ( newline ) ) |
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OD |
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END</lang> |
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{{out}} |
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<pre> |
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1 1 1 2 1 2 2 2 2 3 |
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3 3 2 3 2 4 4 2 3 4 |
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3 4 5 4 3 5 3 4 6 3 |
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5 6 2 5 6 5 5 7 4 5 |
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8 5 4 9 4 5 7 3 6 8 |
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5 6 8 6 7 10 6 6 12 4 |
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5 10 3 7 9 6 5 8 7 8 |
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11 6 5 12 4 8 11 5 8 10 |
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5 6 13 9 6 11 7 7 14 6 |
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8 13 5 8 11 7 9 13 8 9 |
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G(1000000): 5402 |
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</pre><span style="font-size 8px"><pre> |
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+.=* |
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| +*- |
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| +=-. |
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| ...=-. |
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| .-+.... |
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| .=.- . . |
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| ..-.-... |
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| .-. + -. |
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| .-- ... .. |
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| ...+. . - |
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+ .+.- .. . |
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| + + .. . . |
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| . -+. . - |
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| -.- . . - . |
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| + ... .. . . |
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| .--.. - . |
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| .. ..- . .. . |
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| -+ . .. . . |
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| - .. .- - . |
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| . ..-. . . . . |
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+ .+ - . .. . |
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| . -..- . - |
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| . +- . . . . |
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| ..-.. .. .. |
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| . . +. . .- |
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| - -- . . . . |
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| . .-. . . .. . |
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| .+ . .. - . |
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| ..-. . . . . . |
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| -. -. . . . . |
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+ .... ... -. |
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| . . ..... . . . |
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| . ... . . . . . . |
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| . .... - . . . |
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| . . + . . - . |
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| ...... . . . . |
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| .+ .. . . - |
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| .. ..- . . . . |
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| ..-. . ... . |
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| -. .. .. . . . |
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+ . -.. - . . . |
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| ... .- . .. . |
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| . .-.. . .. . |
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| . -.. . . . . . |
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| .-.. . . . . . |
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| - .. . . - .. |
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| .+ - . . . . |
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| ... .. . .. . . |
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| .-.. .. . . . |
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| . - . . . . . . . |
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+ + . . . . . . . |
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| - .. ... . . . |
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| .+ . . . . . . |
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| .. -. . . .. . |
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| - .. . . . .. . |
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| . ...- . . . . |
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| .. .- . . . . . |
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| .. . . .. . . . . |
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| .. - ... . . . |
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| - .- . . . . . |
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+ .... .. . .. . |
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| . - - . . . . . |
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| .. - . . .. . . |
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| .. .-- . - |
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| . .. - . . . . . |
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| .- .. . - . . |
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| .. -.. . . . . |
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| .- .. . . . . . |
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| . =. . .. . |
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| - + . . .. . |
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+ . . . . . . . .. . |
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| -- . . . . . . |
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| . ... .. . . .. |
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| . ... .. . . . . |
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| . ... .. . - . |
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| . ..- . . . . . |
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| . .-. . ... . |
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| . .. . .. . . . . |
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| . .. .. . . . . . |
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| ..... . . . . . |
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+ . . . . . . . - . |
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| . - . - . . . . |
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| .-- . . . . . |
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| - . .. . .. . . |
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| . . . .. . . . .. |
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| . .. - . . . . . |
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| . . . . .. . . . . |
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| - . . . . . . - |
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| ... ... . . . . |
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| . . .. - . . . . |
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+ .- - . . - . |
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| . ... .. . . . . |
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| -. - . - . . |
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| . . . . . . . . . . |
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| . . .- .. . . . |
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| . - .- . . . . |
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| . - .. . . . . . |
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| . ... .. . . . . |
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| . . -. . . . . . |
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</pre></span> |
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=={{header|Arturo}}== |
=={{header|Arturo}}== |
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Here, you can find the result of the visualization - or the "Goldbach's comet": [https://i.ibb.co/JvLDRc0/Screenshot-2022-05-07-at-11-35-23.png 2D-chart of all G values up to 2000] |
Here, you can find the result of the visualization - or the "Goldbach's comet": [https://i.ibb.co/JvLDRc0/Screenshot-2022-05-07-at-11-35-23.png 2D-chart of all G values up to 2000] |
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=={{header|Julia}}== |
=={{header|Julia}}== |
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