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Ingy döt Net
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46
Task/Totient-function/Agena/totient-function.agena
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46
Task/Totient-function/Agena/totient-function.agena
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scope # Totient function
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# returns the number of integers k where 1 <= k <= n that are mutually prime to n
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local procedure totient( n :: number ) :: number
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if n < 3 then result := 1
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elif n = 3 then result := 2
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else
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result := n;
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local v, i := n, 2;
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while i * i <= v do
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if v mod i = 0 then
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while v mod i = 0 do v \:= i od;
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result -:= result \ i
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fi;
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if i = 2 then
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i := 1
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fi;
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i +:= 2
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od;
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if v > 1 then result -:= result \ v fi;
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fi;
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return result
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end;
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# show the totient function values for the first 25 integers
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io.write( " n phi(n) remarks\n" );
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for n to 25 do
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local constant tn := totient( n );
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printf( "%2d: %5d%s\n", n, tn, if tn = n - 1 and tn <> 0 then " n is prime" else "" fi )
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od;
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# use the totient function to count primes
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local n100, n1_000, n10_000, n100_000 := 0, 0, 0, 0;
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for n to 100_000 do
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if totient( n ) = n - 1 then
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if n <= 100 then n100 +:= 1 fi;
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if n <= 1000 then n1_000 +:= 1 fi;
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if n <= 10000 then n10_000 +:= 1 fi;
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if n <= 100000 then n100_000 +:= 1 fi
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fi
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od;
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printf( "There are %6d primes below 100\n", n100 );
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printf( "There are %6d primes below 1 000\n", n1_000 );
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printf( "There are %6d primes below 10 000\n", n10_000 );
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printf( "There are %6d primes below 100 000\n", n100_000 )
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end
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54
Task/Totient-function/Fortran/totient-function.f
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54
Task/Totient-function/Fortran/totient-function.f
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program totient_function
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implicit none
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integer, parameter :: M = 100000
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integer :: i, j
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integer, dimension(1:M) :: phi
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character(len=10) :: is_prime
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integer :: count100, count1000, count10000, count100000
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! Initialize phi array
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do i = 1, M
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phi(i) = i
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end do
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! Compute totient using sieve method
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do i = 2, M
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if (phi(i) == i) then ! i is prime
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do j = i, M, i
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phi(j) = (phi(j) / i) * (i - 1)
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end do
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end if
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end do
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! Display for the first 25 integers
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print*,'n phi prime'
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print*,repeat('-',30)
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do i = 1, 25
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if (phi(i) == i - 1) then
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is_prime = 'prime'
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else
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is_prime = 'not prime'
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end if
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print "(i0,t10,i3,t20,a)", i, phi(i), trim(is_prime)
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end do
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! Count primes up to specified limits
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count100 = 0
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count1000 = 0
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count10000 = 0
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count100000 = 0
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do i = 2, M
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if (phi(i) == i - 1) then
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if (i <= 100) count100 = count100 + 1
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if (i <= 1000) count1000 = count1000 + 1
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if (i <= 10000) count10000 = count10000 + 1
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count100000 = count100000 + 1
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end if
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end do
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print *, 'Count of primes up to 100:', count100
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print *, 'Count of primes up to 1,000:', count1000
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print *, 'Count of primes up to 10,000:', count10000
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print *, 'Count of primes up to 100,000:', count100000
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end program totient_function
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@ -22,23 +22,20 @@ do
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io.write( " n phi(n) remarks\n" )
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for n = 1,25 do
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local tn = totient( n )
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io.write( string.format( "%2d", n ), ": ", string.format( "%5d", tn )
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, ( tn == n - 1 and tn ~= 0 and " n is prime" or "" )
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, "\n"
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)
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io.write( string.format( "%2d: %5d%s\n", n, tn, ( tn == n - 1 and tn ~= 0 and " n is prime" or "" ) ) )
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end
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-- use the totient function to count primes
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local n100, n1000, n10000, n100000 = 0, 0, 0, 0
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local n100, n1_000, n10_000, n100_000 = 0, 0, 0, 0
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for n = 1,100000 do
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if totient( n ) == n - 1 then
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if n <= 100 then n100 = n100 + 1 end
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if n <= 1000 then n1000 = n1000 + 1 end
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if n <= 10000 then n10000 = n10000 + 1 end
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if n <= 100000 then n100000 = n100000 + 1 end
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if n <= 100 then n100 = n100 + 1 end
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if n <= 1000 then n1_000 = n1_000 + 1 end
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if n <= 10000 then n10_000 = n10_000 + 1 end
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if n <= 100000 then n100_000 = n100_000 + 1 end
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end
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end
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io.write( "There are ", string.format( "%6d", n100 ), " primes below 100\n" )
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io.write( "There are ", string.format( "%6d", n1000 ), " primes below 1 000\n" )
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io.write( "There are ", string.format( "%6d", n10000 ), " primes below 10 000\n" )
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io.write( "There are ", string.format( "%6d", n100000 ), " primes below 100 000\n" )
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io.write( string.format( "There are %6d primes below 100\n", n100 ) )
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io.write( string.format( "There are %6d primes below 1 000\n", n1_000 ) )
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io.write( string.format( "There are %6d primes below 10 000\n", n10_000 ) )
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io.write( string.format( "There are %6d primes below 100 000\n", n100_000 ) )
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end
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33
Task/Totient-function/Pluto/totient-function.pluto
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33
Task/Totient-function/Pluto/totient-function.pluto
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local function totient(n)
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local tot = n
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local i = 2
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while i * i <= n do
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if n % i == 0 then
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while n % i == 0 do n //= i end
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tot -= tot // i
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end
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if i == 2 then i = 1 end
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i += 2
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end
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if n > 1 do tot -= tot // n end
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return tot
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end
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print(" n phi prime")
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print("---------------")
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local count = 0
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for n = 1, 25 do
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local tot = totient(n)
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local isPrime = (n - 1) == tot
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if isPrime then ++count end
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print(string.format("%2d %2d %s", n, tot, isPrime))
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end
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print("\nNumber of primes up to 25 = " .. count)
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for n = 26, 100_000 do
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local tot = totient(n)
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if tot == n - 1 then ++count end
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if n == 100 or n == 1_000 or n % 10_000 == 0 then
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local ns = string.format("%-6d", n)
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print($"\nNumber of primes up to {ns} = {count}")
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end
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end
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