Add tasks for all the new languages
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Tina Müller
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; the first twenty primes
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(primes 20)
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→ { 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 }
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; a stream to generate primes from a
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(define (primes-from a)
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(let ((p (next-prime a)))
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(stream-cons p (primes-from p))))
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; primes between 100,150
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(for/list ((p (primes-from 100))) #:break (> p 150) p)
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→ (101 103 107 109 113 127 131 137 139 149)
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; the built-in function (primes-pi )counts the number of primes < a
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; count in [7700 ... 8000]
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(- (primes-pi 8000) (primes-pi 7700) → 30
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; nth-prime
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(nth-prime 10000) → 104729
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;; big ones
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(lib 'bigint)
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(define (p-digits n)
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(printf "(next-prime %d ! ) has %d digits" n
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(number-length (next-prime (factorial n )))))
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(next-prime 0! ) has 1 digits
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(next-prime 10! ) has 7 digits
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(next-prime 100! ) has 158 digits
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(next-prime 200! ) has 375 digits
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(next-prime 300! ) has 615 digits
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(next-prime 400! ) has 869 digits ;; 9400 msec (FireFox)
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; is prime (1 + 116!) ?
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(prime? (1+ (factorial 116))) → #t
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@ -0,0 +1,100 @@
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' FB 1.05.0
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Enum SieveLimitType
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number
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between
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countBetween
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End Enum
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Sub printPrimes(low As Integer, high As Integer, slt As SieveLimitType)
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If high < low OrElse low < 1 Then Return ' too small
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If slt <> number AndAlso slt <> between AndAlso slt <> countBetween Then Return
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If slt <> number AndAlso (low < 2 OrElse high < 2) Then Return
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If slt <> number AndAlso high > 1000000000 Then Return ' too big
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If slt = number AndAlso high > 50000000 Then Return ' too big
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Dim As Integer n
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If slt = number Then
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n = 20 * high '' big enough to accomodate 50 million primes to which this procedure is limited
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Else
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n = high
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End If
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Dim a(2 To n) As Boolean '' only uses 1 byte per element
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For i As Integer = 2 To n : a(i) = True : Next '' set all elements to True to start with
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Dim As Integer p = 2, q
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' mark non-prime numbers by setting the corresponding array element to False
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Do
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For j As Integer = p * p To n Step p
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a(j) = False
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Next j
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' look for next True element in array after 'p'
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q = 0
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For j As Integer = p + 1 To Sqr(n)
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If a(j) Then
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q = j
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Exit For
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End If
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Next j
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If q = 0 Then Exit Do
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p = q
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Loop
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Select Case As Const slt
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Case number
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Dim count As Integer = 0
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For i As Integer = 2 To n
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If a(i) Then
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count += 1
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If count >= low AndAlso count <= high Then
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Print i; " ";
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End If
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If count = high Then Exit Select
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End If
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Next
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Case between
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For i As Integer = low To high
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If a(i) Then
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Print i; " ";
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End if
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Next
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Case countBetween
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Dim count As Integer = 0
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For i As Integer = low To high
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If a(i) Then count += 1
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Next
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Print count;
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End Select
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Print
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End Sub
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Print "The first 20 primes are :"
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Print
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printPrimes(1, 20, number)
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Print
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Print "The primes between 100 and 150 are :"
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Print
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printPrimes(100, 150, between)
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Print
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Print "The number of primes between 7700 and 8000 is :";
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printPrimes(7700, 8000, countBetween)
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Print
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Print "The 10000th prime is :";
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Dim t As Double = timer
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printPrimes(10000, 10000, number)
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Print "Computed in "; CInt((timer - t) * 1000 + 0.5); " ms"
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Print
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Print "The 1000000th prime is :";
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t = timer
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printPrimes(1000000, 1000000, number)
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Print "Computed in ";CInt((timer - t) * 1000 + 0.5); " ms"
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Print
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Print "The 50000000th prime is :";
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t = timer
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printPrimes(50000000, 50000000, number)
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Print "Computed in ";CInt((timer - t) * 1000 + 0.5); " ms"
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Print
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Print "Press any key to quit"
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Sleep
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@ -0,0 +1,38 @@
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see "first twenty primes : "
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i = 1
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nr = 0
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while i <= 20
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nr += 1
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if isPrime(nr) see " " + nr i += 1 ok
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end
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see "primes between 100 and 150 : "
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for nr = 100 to 150
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if isPrime(nr) see " " + nr ok
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next
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see nl
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see "primes between 7,700 and 8,000 : "
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i = 0
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for nr = 7700 to 8000
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if isPrime(nr) i += 1 ok
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next
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see i + nl
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see "The 10,000th prime : "
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i = 1
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nr = 0
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while i <= 10000
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nr += 1
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if isPrime(nr) i += 1 ok
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end
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see nr + nl
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func isPrime n
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if n <= 1 return false ok
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if n <= 3 return true ok
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if (n & 1) = 0 return false ok
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for t = 3 to sqrt(n) step 2
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if (n % t) = 0 return false ok
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next
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return true
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var nt = frequire('ntheory')
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say ("First 20: ", nt.primes(nt.nth_prime(20)).join(' '))
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say ("Between 100 and 150: ", nt.primes(100,150).join(' '))
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say (nt.prime_count(7700,8000), " primes between 7700 and 8000")
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say ("10,000th prime: ", nt.nth_prime(10_000))
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@ -0,0 +1,9 @@
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# Recent versions of jq include the following definition:
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# until/2 loops until cond is satisfied,
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# and emits the value satisfying the condition:
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def until(cond; next):
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def _until:
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if cond then . else (next|_until) end;
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_until;
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def count(cond): reduce .[] as $x (0; if $x|cond then .+1 else . end);
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# Is the input integer a prime?
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# "previous" must be the array of sorted primes greater than 1 up to (.|sqrt)
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def is_prime(previous):
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. as $in
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| (previous|length) as $plength
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| [false, 0] # state: [found, ix]
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| until( .[0] or .[1] >= $plength;
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[ ($in % previous[.[1]]) == 0, .[1] + 1] )
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| .[0] | not ;
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# extend_primes expects its input to be an array consisting of
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# previously found primes, in order, and extends that array:
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def extend_primes:
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if . == null or length == 0 then [2]
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else . as $previous
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| if . == [2] then [2,3]
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else . + [(2 + .[length-1]) | until( is_prime($previous) ; . + 2)]
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end
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end;
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# If . is an integer > 0 then produce an array of . primes;
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# otherwise emit an unbounded stream of primes:
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def primes:
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. as $n
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| if type == "number" and $n > 0 then
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null | until( length == $n; extend_primes )
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else [2] | recurse(extend_primes) | .[length - 1]
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end;
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# Primes up to and possibly including n:
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def primes_upto(n):
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until( .[length-1] > n; extend_primes )
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| if .[length-1] > n then .[0:length-1] else . end;
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@ -0,0 +1,9 @@
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"First 20 primes:", (20 | primes), "",
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"Primes between 100 and 150:",
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(primes_upto(150) | map(select( 100 < .))), "",
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"The 10,000th prime is \( 10000 | primes | .[length - 1] )", "",
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(( primes_upto(8000) | count( . > 7700) | length) as $length
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| "There are \($length) primes twixt 7700 and 8000.")
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@ -0,0 +1,10 @@
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$ jq -r -c -n -f Extensible_prime_generator.jq
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First 20 primes:
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[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71]
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Primes between 100 and 150:
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[101,103,107,109,113,127,131,137,139,149]
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The 10,000th prime is 104729
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There are 30 primes twixt 7700 and 8000.
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