wheel = [2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,
         4,8,6,4,6,2,4,6,2,6,6,4,2,4,6,2,6,4,2,4,2,10,2,10]
wsize = 48
 
def primes(): 
	yield from (2, 3, 5, 7)
	yield from wsieve()
 
def wsieve():       # wheel-sieve, by Will Ness. cf. ideone.com/WFv4f
    yield 11        # cf. http://stackoverflow.com/a/10733621/849891     
    mults = {}      #     http://stackoverflow.com/a/19391111/849891
    ps = wsieve()   # base primes
    p = next(ps)    # 11
    psq = p*p       # 121
    c = 11          # the last Candidate
    i = 0           # position on the wheel for next c: 11+2 =: 13
    cbase = 11      # base coprimes stream, to gen the mults for primes in it
    ibase = 0       # position on wheel for cbase==p
    while True:
        c += wheel[i]                 # next candidate from coprimes
        i = (i+1) % wsize             #   on the wheel
        if c not in mults:            # c's not a multiple of any base prime:
            if c < psq:               #   hence, a prime 
                yield c ; continue    #                  ; or
            else:   # (c==psq)        #   is the next base prime's square:
                while not cbase == p:        # skip on base coprimes until
                	cbase += wheel[ibase]    #  the base prime from rec supply
                	ibase = (ibase+1) % wsize
                # map (p*) $ scanl (+) p (d:w) =
                #          = scanl (\c d->c+p*d) (p*p) (d:w) 
                # add(mults, c, ibase, p)    # add NEXT mult of p after c==psq
                j = ibase ; pbase = p        #   go from ibase on the wheel
                p = next(ps) ; psq = p*p
        else:                         # `c` is a mult of prev-seen base prime:
            (j,pbase) = mults.pop(c)        
            # add(mults, c, j, pbase)        # add NEXT mult of pbase after c
        m = c + pbase*wheel[j] ; j = (j+1) % wsize
        while m in mults:  
            m += pbase*wheel[j] ; j = (j+1) % wsize
        mults[m] = (j,pbase)                 #            into the mults dict
 
import itertools       # 100K  0.42s-8.7MB          800K  4.00s-8.7MB n^1.1
                       # 200K  0.88s-8.7MB          1M    5.10s-8.7MB
if True:               # 400K  1.88s-8.7MB  n^1.1   2M   10.88s-8.7MB n^1.1
    n = 800000
    print(n) 
    print( list( itertools.islice( (p for p in primes() ), n-1, n+1)))   

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