def find1():
# take so long
for n in genprime():
if ispandigital(n):
print n
if n > 987654321:
break
def sum1(n):
# a bit slow
s=0
for p in genprime():
if p > n:
break
s+=p
return s
def goldbach():
gp = genprime()
p = gp.next()
q = gp.next()
while True:
for com in xrange(p+2,q,2):
if not isop(com):
return com
p = q
q = gp.next()
def findmostCP(LIMITS):
primes = []
sop = 0
gp = genprime()
while sop < LIMITS:
p = gp.next()
primes.append(p)
sop += p
for n in range(1,len(primes)):
for i in range(n+1):
s = sum(primes[i:len(primes)-n+i])
if s < LIMITS and isprime(s):
return s
def findR2(a, b):
# phi = pi(n*(1-1/p))
gp = genprime()
r, l = b, a
d = 1
while True:
p = gp.next()
rn = r * (p - 1)
ln = l * p
dn = d * p
# find the most 2*3*5*...value
if rn * dn < ln * (dn - 1):
# test small values
for i in xrange(2, p):
if r * d * i < l * (d * i - 1):
return d * i
r = rn
l = ln
d = dn
return 0
if n!=s:
return False
return True
def isperm(l):
if len(l) < 1:
return False
k = [sorted(str(i)) for i in l]
d = k[0]
for p in k:
if p != k:
return False
return True
primedic = {}
for n in genprime():
if n > 10000:
break
if n > 1000:
s = int(''.join(sorted(str(n))))
if s not in primedic:
primedic[s] = []
primedic[s].append(n)
for numsl in primedic.values():
for nums in combinations(numsl,3):
if isacc(nums):
print nums
#! /usr/bin/env python
from eulerutils import genprime,ispermutation
from sys import exit
primes = []
# for sqrt(10**7) ~ 50%
for p in genprime():
if p > 5000:
break
if p > 2000:
primes.append(p)
print 'initial done'
primes.reverse()
res = []
for i in xrange(len(primes)):
for j in xrange(i,len(primes)):
p = primes[i]
q = primes[j]
if p*q > 10**7:
continue
if p!=q:
phi = (p-1)*(q-1)
else:
phi = p*(p-1)
if ispermutation(p*q,phi):
res.append((float(p*q)/phi,p*q))
#! /usr/bin/env python
from eulerutils import genprime
gp = genprime()
for i in xrange(10001):
p = gp.next()
print p