#!/usr/bin/python
import eulerlib
primes = eulerlib.sieveOfEratosthenes( int( 1e6 ) )
truncatablePrimes = []
for prime in primes:
if eulerlib.isTruncatable( prime, primes ) and prime not in [2, 3, 5, 7]:
truncatablePrimes.append( prime )
if len( truncatablePrimes ) == 11:
break
print sum( truncatablePrimes )
#!/usr/bin/python
from eulerlib import sieveOfEratosthenes
from eulerlib import howManyPrimes
n = 1000
print "for n = 1000, n^2 = ", n ** 2
p = sieveOfEratosthenes(n)
print "for p = ", len(p), ", p^2 = ", len(p) ** 2
p.reverse()
p.append(1)
maxPrime = 0
aMax = 0
bMax = 0
for ii in p:
for kk in p:
howMany1 = howManyPrimes(ii, kk)
howMany2 = howManyPrimes(-ii, kk)
howMany3 = howManyPrimes(ii, -kk)
howMany4 = howManyPrimes(-ii, -kk)
howManyMax = max([howMany1, howMany2, howMany3, howMany4])
if howManyMax > maxPrime:
maxPrime = howManyMax
aMax = ii
bMax = kk
print maxPrime, ', ', aMax, ', ', bMax, ', ', aMax, ', ', bMax
#!/usr/bin/python
import eulerlib
if __name__ == '__main__':
'''
http://mathworld.wolfram.com/DecimalExpansion.html
http://en.wikipedia.org/wiki/Repeating_decimal
http://mathworld.wolfram.com/DiscreteLogarithm.html
http://en.wikipedia.org/wiki/Discrete_logarithm
'''
dMax = 1000
primes = eulerlib.sieveOfEratosthenes(dMax)
primes.remove(2)
primes.remove(5)
primes.reverse()
kMax = 1
pMax = primes[0]
for p in primes:
k = 1
while (pow(10, k) % p) != 1:
k += 1
if k > kMax:
kMax = k
pMax = p
print 'Repeating length: ', kMax
#!/usr/bin/python
from eulerlib import sieveOfEratosthenes
from eulerlib import rotateInt
from eulerlib import nDigits
primes = sieveOfEratosthenes(1000000)
#primes = sieveOfEratosthenes(100)
ncircPrimes = 0
digits = [[], [], [], [], [], []]
for ii in primes:
n = nDigits( ii )
digits[n - 1].append( ii )
for n in range(len(digits)): # Loop over each bucket
print n
for m in digits[n]: # Loop over the integers in each bucket
isCircPrime = True
for l in range(n + 1): # Loop over the rotations of each number
if rotateInt(m, l) not in digits[n]:
break
else:
ncircPrimes = ncircPrimes + 1
print ncircPrimes
