Hi all!
Here is a version which does not use the p: verb. It is more useful as
description of the algorithm. It is also probably less wasteful of
computer resources.
Cheers,
Erling
Prime=: [: -. [: +./0 = [ | ]
(,2) Prime 3
NB. 1
2 3 Prime 4
NB. 0
2 3 Prime 5
NB. 1
2 3 5 Prime 6
NB. 0
PrimesUntil=: 3 : 0
primes=.i.0
n=. 2 + i. y - 1
for_i. n do.
primes=.primes,(primes Prime i) # i
end.
primes
)
PrimesUntil 5
NB. 2 3 5
PrimesUntil 10
NB. 2 3 5 7
PrimesUntil 11
NB. 2 3 5 7 11
PrimesInRange=: 4 : 0
n=. PrimesUntil y
(n >: x)# n
)
7 PrimesInRange 11
NB. 7 11
7 PrimesInRange 10
NB. 7
8 PrimesInRange 10
NB. i.0
AddStartRangeIfNotThere=: (([ ~: 1 {. ]) # [) , ]
3 AddStartRangeIfNotThere 3 5 7 11
NB. 3 5 7 11
8 AddStartRangeIfNotThere i.0
NB. 8
AddEndRangeIfNotThere=: ] , ([ ~: _1 {. ]) # [
11 AddEndRangeIfNotThere 3 5 7 11
NB. 3 5 7 11
10 AddEndRangeIfNotThere 8
NB. 8 10
SequenceLengths=: 1 + (1 }. ]) - _1 }. ]
SequenceLengths 3 5 7 11
NB.3 3 5
SequenceLengths 8 10
NB. 3
FirstInLongestSequence=: '' $ (([ = [: >./ [) , 0:) # ]
3 3 5 FirstInLongestSequence 3 5 7 11
NB. 7
3 FirstInLongestSequence 8 10
NB. 8
SequenceIndices=: ] + [: i. [: >./ [
3 3 5 SequenceIndices 7
NB. 7 8 9 10 11
(,3) SequenceIndices 8
NB. 8 9 10
DropFirstIfPrime=: ((1 {. ]) e. [) }. ]
7 11 DropFirstIfPrime 7 8 9 10 11
NB. 8 9 10 11
(i.0) DropFirstIfPrime 8 9 10
NB. 8 9 10
DropLastIfPrime=: ([: -(_1 {. ]) e. [) }. ]
(,11)DropLastIfPrime 8 9 10 11
NB. 8 9 10
(i.0)DropLastIfPrime 8 9 10
f=: 4 : 0
NB. Find the longest sequence of non-primes in a range
NB. x and y are the range limits
primesInRange =. x PrimesInRange y
NB. Add range limits if they are not primes and then already there
rangeLimits =. y AddEndRangeIfNotThere x AddStartRangeIfNotThere
primesInRange
NB. The lengths of the possible sequences, including both sequence limits
sequenceLengths =. SequenceLengths rangeLimits
NB. The first element of the longest sequence
firstInLongestSequence=.sequenceLengths FirstInLongestSequence rangeLimits
NB. The longest range including it's both limits
longestRange =. sequenceLengths SequenceIndices firstInLongestSequence
NB. Drop the range limits if they are primes
primesInRange DropLastIfPrime primesInRange DropFirstIfPrime longestRange
)
s=: 10 f 100
s
>./90 91 92 93 94 95 96 = s
s=: 1 f 2
>./s = 1
s=: 2 f 3
0 = $ s
s=: 8 f 9
>./s = 8 9
s=: 7 f 8
>./s = 8
s=: 10 f 11
>./s = 10
s=: 7 f 11
>./s = 8 9 10
s=: 200 f 300
s
>./0 = 1 p: s
1 = 1 p: _1 + 1 {. s
1 = 1 p: 1 + _1 {. s
s=: 2000 f 3000
s
>./0 = 1 p: s
1 = 1 p: _1 + 1 {. s
1 = 1 p: 1 + _1 {. s
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