36 lines
1.4 KiB
Python
36 lines
1.4 KiB
Python
def wsieve(): # ideone.com/mqO25A
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wh11 = [ 2,4,2,4,6,2,6,4,2,4,6,6, 2,6,4,2,6,4,6,8,4,2,4,2,
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4,8,6,4,6,2,4,6,2,6,6,4, 2,4,6,2,6,4,2,4,2,10,2,10]
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cs = accumulate( chain( [11], cycle( wh11)))
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yield( next( cs)) # cf. ideone.com/WFv4f
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ps = wsieve() # codereview.stackexchange.com/q/92365/9064
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p = next(ps) # 11 stackoverflow.com/q/30553925/849891
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psq = p*p # 121
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D = dict( zip( accumulate( chain( [0], wh11)), count(0))) # start from
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mults = {}
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for c in cs:
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if c in mults:
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wheel = mults.pop(c)
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elif c < psq:
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yield c ; continue
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else: # c==psq: map (p*) (roll wh from p) = roll (wh*p) from (p*p)
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x = [p*d for d in wh11]
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i = D[ (p-11) % 210]
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wheel = accumulate( chain( [psq+x[i]], cycle( x[i+1:] + x[:i+1])))
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p = next(ps) ; psq = p*p
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for m in wheel:
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if not m in mults:
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break
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mults[m] = wheel
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def primes():
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yield from (2, 3, 5, 7)
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yield from wsieve()
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print( list( islice( primes(), 0, 20)))
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print( list( takewhile( lambda x: x<150,
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dropwhile( lambda x: x<100, primes()))))
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print( len( list( takewhile( lambda x: x<8000,
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dropwhile( lambda x: x<7700, primes())))))
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print( list( islice( primes(), 10000-1, 10000))[0])
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