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Initial data commit

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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 72d218235f
commit f23f22d71c
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Task/Totient-function/ALGOL-68/totient-function.alg Normal file
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BEGIN
# returns the number of integers k where 1 <= k <= n that are mutually prime to n #
PROC totient = ( INT n )INT:
IF n < 3 THEN 1
ELIF n = 3 THEN 2
ELSE
INT result := n;
INT v := n;
INT i := 2;
WHILE i * i <= v DO
IF v MOD i = 0 THEN
WHILE v MOD i = 0 DO v OVERAB i OD;
result -:= result OVER i
FI;
IF i = 2 THEN
i := 1
FI;
i +:= 2
OD;
IF v > 1 THEN result -:= result OVER v FI;
result
FI # totient # ;
# show the totient function values for the first 25 integers #
print( ( " n phi(n) remarks", newline ) );
FOR n TO 25 DO
INT tn = totient( n );
print( ( whole( n, -2 ), ": ", whole( tn, -5 ), IF tn = n - 1 AND tn /= 0 THEN " n is prime" ELSE "" FI, newline ) )
OD;
# use the totient function to count primes #
INT n100 := 0, n1000 := 0, n10000 := 0, n100000 := 0;
FOR n TO 100 000 DO
IF totient( n ) = n - 1 THEN
IF n <= 100 THEN n100 +:= 1 FI;
IF n <= 1 000 THEN n1000 +:= 1 FI;
IF n <= 10 000 THEN n10000 +:= 1 FI;
IF n <= 100 000 THEN n100000 +:= 1 FI
FI
OD;
print( ( "There are ", whole( n100, -6 ), " primes below 100", newline ) );
print( ( "There are ", whole( n1000, -6 ), " primes below 1 000", newline ) );
print( ( "There are ", whole( n10000, -6 ), " primes below 10 000", newline ) );
print( ( "There are ", whole( n100000, -6 ), " primes below 100 000", newline ) )
END