Goldbach's comet: Difference between revisions

Content added Content deleted
(→‎{{header|ALGOL 68}}: Simplified also no need to calculate G(n) for all n to 000 000 - just need 2 000!! Corrected plot)
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# of prime pairs that sum to n, n even and > 2 #
# of prime pairs that sum to n, n even and > 2 #
# generates an ASCII scatter plot of G(n) up to G(2000) #
# generates an ASCII scatter plot of G(n) up to G(2000) #
# (Goldbach's Comet) #
PR read "primes.incl.a68" PR # include prime utilities #
PR read "primes.incl.a68" PR # include prime utilities #
INT max number = 1 000 000; # maximum number we will consider #
INT max prime = 1 000 000; # maximum number we will consider #
INT max plot = 2 000; # maximum G value for the comet #
# get a list of primes up to max number #
[]INT prime list = EXTRACTPRIMESUPTO max number FROMPRIMESIEVE PRIMESIEVE max number;
[]BOOL prime = PRIMESIEVE max prime; # sieve of primes to max prime #
[ 1 : max number ]INT g2; # table of G values: g2[n] = G(2n) #
[ 0 : max plot ]INT g2; # table of G values: g2[n] = G(2n) #
# construct the table of G values #
# construct the table of G values #
FOR n TO UPB g2 DO g2[ n ] := 0 OD;
FOR n FROM LWB g2 TO UPB g2 DO g2[ n ] := 0 OD;
g2[ 2 ] := 1; # 4 is the only sum of two even primes #
g2[ 4 ] := 1; # 4 is the only sum of two even primes #
FOR n FROM 2 TO UPB prime list DO
FOR p FROM 3 BY 2 TO max plot OVER 2 DO
INT p = prime list[ n ];
IF prime[ p ] THEN
g2[ p ] +:= 1;
g2[ p + p ] +:= 1;
FOR m FROM n + 1 TO UPB prime list
FOR q FROM p + 2 BY 2 TO max plot - p DO
WHILE INT sum = p + prime list[ m ];
IF prime[ q ] THEN
sum <= max number
g2[ p + q ] +:= 1
DO
FI
g2[ sum OVER 2 ] +:= 1
OD
OD
FI
OD;
OD;
# show the first hundred G values #
# show the first hundred G values #
FOR n FROM 2 TO 101 DO
INT c := 0;
FOR n FROM 4 BY 2 TO 202 DO
print( ( whole( g2[ n ], -4 ) ) );
print( ( whole( g2[ n ], -4 ) ) );
IF ( n - 1 ) MOD 10 = 0 THEN print( ( newline ) ) FI
IF ( c +:= 1 ) = 10 THEN print( ( newline ) ); c := 0 FI
OD;
OD;
# G( 1 000 000 ) #
# show G( 1 000 000 ) #
INT gm := 0;
print( ( "G(", whole( max number, 0 ), "): "
, whole( g2[ max number OVER 2 ], 0 )
FOR p FROM 3 TO max prime OVER 2 DO
, newline
IF prime[ p ] THEN
)
IF prime[ max prime - p ] THEN
);
gm +:= 1
FI
FI
OD;
print( ( "G(", whole( max prime, 0 ), "): ", whole( gm, 0 ), newline ) );
# find the maximum value of G up to the maximum plot size #
# find the maximum value of G up to the maximum plot size #
INT max plot = 2000;
INT max g := 0;
INT max g := 0;
FOR n FROM 2 BY 2 TO max plot DO
FOR n TO max plot OVER 2 DO
IF g2[ n ] > max g THEN max g := g2[ n ] FI
IF g2[ n ] > max g THEN max g := g2[ n ] FI
OD;
OD;
# draw an ASCII scatter plot of G, each position represents 10 G values #
# draw an ASCII scatter plot of G, each position represents 5 G values #
# the vertical axis is n, the horizontal axis is G(n) #
# the vertical axis is n/10, the horizontal axis is G(n) #
INT plot step = 10;
INT plot step = 10;
STRING plot value = " .-+=*%$&#@";
STRING plot value = " .-+=*%$&#@";
FOR g BY plot step TO ( max plot OVER 2 ) - plot step DO
FOR g FROM 0 BY plot step TO max plot - plot step DO
[ 0 : max g ]INT values;
[ 0 : max g ]INT values;
FOR v pos FROM LWB values TO UPB values DO values[ v pos ] := 0 OD;
FOR v pos FROM LWB values TO UPB values DO values[ v pos ] := 0 OD;
INT max v := 0;
INT max v := 0;
FOR g element FROM g TO g + ( plot step - 1 ) DO
FOR g element FROM g BY 2 TO g + ( plot step - 1 ) DO
INT g2 value = g2[ g element ];
INT g2 value = g2[ g element ];
values[ g2 value ] +:= 1;
values[ g2 value ] +:= 1;
IF g2 value > max v THEN max v := g2 value FI
IF g2 value > max v THEN max v := g2 value FI
OD;
OD;
print( ( IF g MOD 100 = 1 THEN "+" ELSE "|" FI ) );
print( ( IF g MOD 100 = 90 THEN "+" ELSE "|" FI ) );
FOR v pos FROM LWB values TO max v DO
FOR v pos FROM 1 TO max v DO # exclude 0 values from the plot #
print( ( plot value[ values[ v pos ] + 1 ] ) )
print( ( plot value[ values[ v pos ] + 1 ] ) )
OD;
OD;
Line 104: Line 109:
G(1000000): 5402
G(1000000): 5402
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</pre></span>
</pre></span>


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