#!/usr/bin/python
from math import log
from math import sqrt
from euler import appendToPrimes
from euler import isPrime
from euler import appendDigitsUnsorted
N = 1000000 # N = 100 #
BASE = 10
primes = []
appendToPrimes(int(sqrt(N)), primes)
# print(primes) # [2, 3, 5, 7]
a = int(sqrt(N))
while a < N:
if isPrime(a, primes):
primes.append(a)
a += 1
# primes contains all primes less than N.
# print(primes) # [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
possibles = [
] # potentially right truncatable: no internal {0,2,4,5,6,8} and no left {0,4,6,8}
for p in primes:
digits = appendDigitsUnsorted(p, [])
if 0 in digits or 4 in digits or 6 in digits or 8 in digits:
continue
digits.pop(0)
#!/usr/bin/python
from euler import isPrime, appendToPrimes
PRIMES = []
UPPER = 10**5
appendToPrimes(UPPER, PRIMES)
twoSquares = [2 * n * n for n in range(0, UPPER)]
n = 3
while True:
while isPrime(n, PRIMES):
n += 2
bad = True
for j in twoSquares:
if n <= j:
break
if isPrime(n - j, PRIMES):
bad = False
n += 2
break
if bad:
break
print(n)
#!/usr/bin/python
import euler
n = 20
primes0 = [2, 3, 5, 7, 11, 13, 17, 19]
primes = []
euler.appendToPrimes(n, primes)
assert primes == primes0
n = 30
euler.appendToPrimes(n, primes)
primes0 += [23, 29]
assert primes == primes0
primeFactors0 = [2, 5, 23]
primeFactors = euler.primeFactors(230, primes)
assert primeFactors == primeFactors0
primeFactors0 = [2, 2, 3, 3]
primeFactors = euler.primeFactors(36, primes)
assert primeFactors == primeFactors0
primePowerFactorization0 = {2: 2, 3: 2}
primePowerFactorization = euler.primePowerFactorization(primeFactors)
assert primePowerFactorization0 == primePowerFactorization
assert (euler.descendingFactorial(5, 2) == 20)
assert (euler.descendingFactorial(5, 3) == 60)
#!/usr/bin/python
import euler
BOUND = 1000 # upper bound for testing primalities
TERMS = 3 # terms in quadratic
primes = set(euler.appendToPrimes(TERMS * BOUND * BOUND))
def quadratic(n, a, b):
return n * n + a * n + b
def isPrime(n, a, b, primes):
return quadratic(n, a, b) in primes
# Returns the count of prime values starting from n = 0.
def countOfPrimes(maximum, a, b, primes):
n = 0
while n <= maximum:
if isPrime(n, a, b, primes):
n += 1
else:
return n
maximumCount = 0 # max counter for primes
a = -BOUND + 1
while a < BOUND - 1:
#!/usr/bin/python
from itertools import permutations
from euler import appendToPrimes
from euler import isPrime
BASE = 10
D = 4 # 2143 is a pandigital prime
PRIMES = []
appendToPrimes(10**5, PRIMES)
maximum = 0
for n in range(D, BASE):
for p in list(permutations(range(1, n + 1))):
i = int(''.join(map(str, p)))
if isPrime(i, PRIMES):
if maximum < i:
maximum = i
print(maximum)
#!/usr/bin/python
from itertools import permutations
from euler import appendToPrimes
BASE = 10
PRIMES = []
appendToPrimes(18, PRIMES)
assert (PRIMES[-1] == 17)
assert (len(PRIMES) == BASE - 3)
def isSubstringDivisible(n):
for i in range(1, BASE - 2):
triple = n % (BASE**3)
if triple % PRIMES[-i] != 0:
return False
n //= BASE
return True
strings = list(permutations(range(0, BASE)))
pandigitals = [int(''.join(map(str, s))) for s in strings]
print(sum([n for n in pandigitals if isSubstringDivisible(n)]))