def run(target=8):
pgen = eu.GenFinder(eu.gen_primes())
# Loop over all prime numbers
for prime_idx in eu.numbers():
curr_prime = pgen[prime_idx]
curr_digits = eu.digits(curr_prime) # digits in current prime
# Get all selections of indices from current digits
for rindices in eu.selections(range(len(curr_digits))):
rzero = 0 in rindices
if len(rindices) == 0:
continue
found_primes = []
work_digs = curr_digits[:] # copy digits of current prime
# Choose the digit which we will insert at each index in rindices (the current selection)
for replacement in range(10):
if replacement == 0 and rzero:
continue
for rindex in rindices:
work_digs[rindex] = replacement
prime_idx = pgen.find(eu.undigits(work_digs))
if prime_idx != -1:
found_primes.append(pgen[prime_idx])
if len(found_primes) >= target:
# print "answer =",min(found_primes),found_primes,rindices
return min(found_primes)
def run():
for power in euler_util.numbers():
start = 10**power
cache = {}
for i in range(start, int(math.ceil(10**(power + 1) / 6.0))):
try:
try:
base_digs = cache[i]
except KeyError:
base_digs = euler_util.digits(i)
base_digs.sort()
cache[i] = base_digs
for x in range(2, 7):
val = x * i
try:
digs = cache[val]
except KeyError:
digs = euler_util.digits(val)
digs.sort()
cache[val] = digs
if not digs == base_digs:
raise Exc
print i
return
except Exc:
pass
def run():
primes = prime_reader.read_primes_default()
last_prime = primes.next()
prime_count = 0
diag_total = 1
current = 1
for ring in eu.numbers(2):
incr = (ring - 1) * 2
for corner in xrange(3):
current = op.iadd(current, incr)
while current > last_prime:
last_prime = primes.next()
if current == last_prime:
prime_count = op.iadd(prime_count, 1)
current = op.add(current, incr)
diag_total = op.iadd(diag_total, 4)
perc = op.div(float(prime_count), diag_total)
# print ring, side_length(ring), last_prime, diag_total, perc
if op.lt(perc, 0.1):
return side_length(ring)
def count_primes(a, b):
sum = 0
for n in euler_util.numbers():
val = f(n, a, b)
while val > primes[-1]:
primes.append(prime_gen.next())
if not val in primes:
return sum
sum += 1
def run():
count = 0
for p in range(1,22):
for x in eu.numbers(1):
l = eu.length(pow(x,p))
if l > p:
break
if l == p:
count += 1
return count
def run():
ts = euler_util.GenFinder(twice_squares())
primes = euler_util.GenFinder(euler_util.gen_primes())
for i in euler_util.numbers(9, 2):
if primes.contains(i):
continue
if not find_sum(i, ts, primes):
print i
return
def run():
sum = 0
for n in range(23, 101):
rgen = euler_util.numbers(1, 1, n + 1)
try:
while combos(n, rgen.next()) <= 1000000:
pass
sum += 1
while combos(n, rgen.next()) > 1000000:
sum += 1
except StopIteration:
pass
def run():
vals = []
for i in euler_util.numbers(1):
factors = [p for p in euler_util.prime_factors(i)]
if len(factors) == 4:
vals.append(i)
print vals
if len(vals) == 4:
print vals
return
else:
vals = []
import euler_util
def complete(x):
y = x[:]
y.sort()
return y == range(1, 10)
max_val = 0
for digits in euler_util.permutations(range(1,10), 4):
base_value = euler_util.undigits(digits)
for i in euler_util.numbers(2):
curr_value = base_value * i
digits += euler_util.digits(curr_value)
if len(digits) > 9:
break
elif len(digits) == 9:
if complete(digits):
val = euler_util.undigits(digits)
# print base_value,i,val
if val > max_val:
max_val = val
break
# print max_val
def run():
for n in eu.numbers():
p = partitions(n)
if p % 1000000 == 0:
return n
def twice_squares():
for i in euler_util.numbers(1):
yield 2 * (i**2)