def euler_51():
"Find the smallest prime which, by changing the same part of the number, can form eight different primes."
from combinatorics import uniqueCombinations
cache = {}
def prime_family_length(n, digits):
if (n, digits) in cache:
return cache[n, digits]
num, nums, count = list(str(n)), [], 0
if len(dict.fromkeys(num[d] for d in digits).keys()) > 1:
return cache.setdefault((n, digits), 0) # The digits must have the same number
for d in range(0 in digits and 1 or 0, 10): # Ensure 0 is not the first digit
for x in digits:
num[x] = str(d)
n = int(''.join(num))
if prime.isprime(n):
count += 1
nums.append(n)
for n in nums:
cache[n, digits] = count
return count
prime._refresh(100000)
n, max, max_count, combos = 10, 0, 0, {}
while max_count < 8:
p = prime.prime(n)
digits = range(0, len(str(p)))
for size in range(1, len(digits)):
patterns = combos.setdefault((len(digits), size),
tuple(tuple(sorted(p)) for p in uniqueCombinations(digits, size)))
for pat in patterns:
count = prime_family_length(p, pat)
if count > max_count: max, max_count = p, count
n += 1
print("Lösung:",p)
def prime_family_length(n, digits):
if cache.has_key((n, digits)): return cache[n, digits]
num, nums, count = list(str(n)), [], 0
if len(dict.fromkeys(num[d] for d in digits).keys()) > 1:
return cache.setdefault((n, digits), 0) # The digits must have the same number
for d in range(0 in digits and 1 or 0, 10): # Ensure 0 is not the first digit
for x in digits: num[x] = str(d)
n = int(''.join(num))
if prime.isprime(n): count += 1
nums.append(n)
for n in nums: cache[n, digits] = count
return count
prime._refresh(100000)
n, max, max_count, combos = 10, 0, 0, {}
while max_count < 8:
p = prime.prime(n)
digits = range(0, len(str(p)))
for size in xrange(1, len(digits)):
patterns = combos.setdefault((len(digits), size),
tuple(tuple(sorted(p)) for p in uniqueCombinations(digits, size)))
for pat in patterns:
count = prime_family_length(p, pat)
if count > max_count: max, max_count = p, count
n += 1
print p