def solve(n=10**6):
# get a list of the primes below n
start = time.time()
primes = eratosthenes(n)
primest = time.time()
# every prime contianing an even digit with the exception of 2 is not
# circular
mark = lambda x : x == 2 or all(c not in str(x) for c in map(str, [0,2,4,6,8]))
# mark all potentially safe primes
sprimes = filter(mark, primes)
markt = time.time()
circs = {}
count = 0
for p in sprimes:
if p not in circs:
val = all(x in sprimes for x in rots(p))
for x in rots(p):
circs[x] = val
if circs[p]:
count += 1
end = time.time()
print ("Solution to PE35: {0}.\nSieve populated in {1}.\nUnsafe primes" +
" filtered in {2}.\nCircular primes found in {3}.\nTot" +
" time: {4}.").format(count, primest - start, markt - primest, end - markt,
end - start)
def solve():
encountered = set()
primes = eratosthenes(10**4)
relevant = set(filter(lambda x : x > 10**3, primes))
ctr = 0
for p in relevant:
# skip primes that you already have dealt with
if p in encountered:
continue
seq = set()
for q in perms(p):
if q in relevant:
encountered.add(q)
seq.add(q)
# don't bother if less then 3 perms of p are primes
if len(seq) >= 3:
seq = sorted(seq)
for sols in indices(len(seq), 3):
i,j,k = map(int, sols)
if seq[k] - seq[j] == seq[j] - seq[i]:
print (seq[i], seq[j], seq[k])
ctr += 1
if ctr == 2:
return
from utils.sieve import eratosthenes
from itertools import combinations
# generates an index list from [0...x-1] of the size y
indices = lambda x, y: combinations(map(str, range(x)), y)
# generate the family from a template
def get_fam(temp):
rs = set()
for i in range(0 if temp[0] != '*' else 1, 10):
rs.add(int(temp.replace('*', str(i))))
return rs
primes = set(eratosthenes(10**6))
def solve():
# generate templates (the last digit should always be odd)
for t in range(101,1000, 2):
for c in indices(5,2):
a = ['*']*6
i, j = map(int,c)
# last digit cannot be a `*`, or at least 4 number wd be composite
a[i], a[j], a[5] = list(str(t))
# assemble string
temp = "".join(a)
fam = get_fam(temp)
if len(fam.intersection(primes)) >= 8:
print fam.intersection(primes)
print "Answer to PE51 is {0}".format(min(fam.intersection(primes)))
return min(fam.intersection(primes))
solve()
