我正在从此处修改一个不确定的Eratosthenes筛子，因此与目前仅检查所有赔率的形式相比，它使用车轮分解来跳过更多合成。

我已经弄清楚了如何产生步骤以达到车轮上所有的间隙。从那里我可以算出我可以用+2代替这些滚轮，但这会导致筛子漏掉素数。这是代码：

from itertools import count, cycle

def dvprm(end):
    "finds primes by trial division. returns a list"
    primes=[2]
    for i in range(3, end+1, 2):
        if all(map(lambda x:i%x, primes)):
            primes.append(i)
    return primes

def prod(seq, factor=1):
    "sequence -> product"
    for i in seq:factor*=i
    return factor

def wheelGaps(primes):
    """returns list of steps to each wheel gap
    that start from the last value in primes"""
    strtPt= primes.pop(-1)#where the wheel starts
    whlCirm= prod(primes)# wheel's circumference

    #spokes are every number that are divisible by primes (composites)
    gaps=[]#locate where the non-spokes are (gaps)
    for i in xrange(strtPt, strtPt+whlCirm+1, 2):
        if not all(map(lambda x:i%x,primes)):continue#spoke 
        else: gaps.append(i)#non-spoke

    #find the steps needed to jump to each gap (beginning from the start of the wheel)
    steps=[]#last step returns to start of wheel
    for i,j in enumerate(gaps):
        if i==0:continue
        steps.append(j - gaps[i-1])
    return steps

def wheel_setup(num):
    "builds initial data for sieve"
    initPrms=dvprm(num)#initial primes from the "roughing" pump
    gaps = wheelGaps(initPrms[:])#get the gaps
    c= initPrms.pop(-1)#prime that starts the wheel

    return initPrms, gaps, c

def wheel_psieve(lvl=0, initData=None):
    '''postponed prime generator with wheels
    Refs:  http://stackoverflow.com/a/10733621
           http://stackoverflow.com/a/19391111'''

    whlSize=11#wheel size, 1 higher prime than
    # 5 gives 2- 3 wheel      11 gives 2- 7 wheel 
    # 7 gives 2- 5 wheel      13 gives 2-11 wheel
    #set to 0 for no wheel

    if lvl:#no need to rebuild the gaps, just pass them down the levels
        initPrms, gaps, c = initData
    else:#but if its the top level then build the gaps
        if whlSize>4:
            initPrms, gaps, c = wheel_setup(whlSize) 
        else:
            initPrms, gaps, c= dvprm(7), [2], 9

    #toss out the initial primes
    for p in initPrms:
        yield p

    cgaps=cycle(gaps)
    compost = {}#found composites to skip

    ps=wheel_psieve(lvl+1, (initPrms, gaps, c))

    p=next(ps)#advance lower level to appropriate square
    while p*p < c:
        p=next(ps)
    psq=p*p

    while True:
        step1 = next(cgaps)#step to next value

        step2=compost.pop(c, 0)#step to next multiple

        if not step2:

            #see references for details
            if c < psq:
                yield c
                c += step1
                continue

            else:
                step2=2*p
                p=next(ps)
                psq=p*p

        d = c + step2
        while d in compost:
            d+= step2
        compost[d]= step2

        c += step1

我正在用它来检查它：

def test(num=100):
    found=[]
    for i,p in enumerate(wheel_psieve(), 1):
        if i>num:break
        found.append(p)

    print sum(found)
    return found

当我将车轮尺寸设置为0时，对于前一百个质数，我得到正确的总和24133，但是当我使用任何其他车轮尺寸时，我最终会丢失质数，错误的总和和合成。即使是2-3轮（使用2和4的交替步骤）也会使筛子漏注。我究竟做错了什么？