def count(arrs, depth):
res = 0
for arr in arrs:
if arr[0] == 0:
continue
if isPrime(prod(arr)):
res += prod(arr)
return res // factorial(depth)
def M(n, digit):
hoeveel = 1
array = n * [digit]
while True:
nrs = permute(array, digit, hoeveel)
for nr in nrs:
if nr[0] == 0:
continue
if isPrime(prod(nr)):
return nrs, hoeveel
hoeveel += 1
def func():
idx = 0
m = len(primes)
while True:
p = primes[idx]
cdx = idx + 1
while cdx < m:
temp = [p]
a1 = digitsum(p) % 3
bdx = cdx
while bdx < m:
new_p = primes[bdx]
if ((digitsum(new_p)) % 3) != a1:
bdx += 1
continue
flag = True
for pr in temp:
front = int(str(pr) + str(new_p))
back = int(str(new_p) + str(pr))
if not (isPrime(front) and isPrime(back)):
flag = False
break
if flag:
temp.append(new_p)
if len(temp) >= 5:
print "FOUND ONE"
print temp
print "Result = " + str(sum(temp))
return
bdx += 1
if len(temp) > 1:
cdx = d[temp[1]] + 1
else:
break
idx += 1
# -*- coding: utf-8 -*-
from eulerTools import isPrime
from datetime import datetime
startTime = datetime.now()
totalcount = 0
truecount = 0
length = 1
start = 1
totalcount += 1
increment = 2
while True:
totalcount += 4
length += 2
for i in range(4):
start += increment
if i == 3:
continue
if isPrime(start):
truecount += 1
increment += 2
if truecount / float(totalcount) < 0.1:
break
print length
print datetime.now() - startTime
#time 12s
# -*- coding: utf-8 -*-
from eulerTools import isPrime
from datetime import datetime
startTime = datetime.now()
#more prime factors => phi(n) is minimal
hoog = 1000000
r = 1
n = 2
while r < hoog:
if isPrime(n):
r *= n
n += 1
r /= (n - 1)
print "res = " + str(r)
print(datetime.now() - startTime)
#5ms
from datetime import datetime
startTime = datetime.now()
from timeit import default_timer as timer
start = timer()
cutoff = int(4e6)
highest_prime_idx = int(ceil(log(cutoff, 3)))
cutoff = cutoff*2 - 1
primes = [2]
list_l = 1
k = 3
while list_l < highest_prime_idx:
if isPrime(k):
primes.append(k)
list_l += 1
k += 2
import heapq
import itertools
#code taken from Python heapq documentation page
pq = [] # list of entries arranged in a heap
entry_finder = {} # mapping of tasks to entries
REMOVED = '<removed-task>' # placeholder for a removed task
counter = itertools.count() # unique sequence count
def add_task(task, priority=0):
'Add a new task or update the priority of an existing task'
if task in entry_finder:
def prime(n):
if n > max_prime:
return isPrime(n)
return n in primes