def problem50(limit):
"""Problem 50 - Prime permutations"""
fpc = pelib.FastPrimeChecker()
# Lazy
tsum = 0
longest = 0
highest_sum = 0
primes = []
for p in pelib.primes_sieve(limit):
primes.append(p)
tsum += p
# print(p,sum)
if tsum - sum(primes[0:len(primes) - longest]) > limit:
break
i = len(primes) - longest
# Subtract from front
for i in range(0, len(primes)):
seqlen = len(primes) - i
if seqlen <= longest:
break
psum = tsum - sum(primes[0:i])
# print(tsum,sum(primes[0:i]),psum,seqlen)
if fpc.is_prime(psum):
longest = seqlen
highest_sum = psum
return highest_sum
def problem49(nr_of_digits, dist):
"""Problem 49 - Prime permutations"""
limit = 10 ** nr_of_digits
fpc = pelib.FastPrimeChecker()
# Lazy
result = 0
skip_set = set()
for p in pelib.primes_sieve(limit):
if p < 10 ** (nr_of_digits - 1) or p in skip_set:
continue
s = set([p])
for pp_arr in itertools.permutations(str(p)):
pp = int("".join(pp_arr))
if len(str(pp)) == nr_of_digits and fpc.is_prime(pp):
s.add(pp)
skip_set.update(s)
if len(s) > 2:
# check
for pe in s:
if s.issuperset([pe, pe + dist, pe + (2 * dist)]) and pe != IGNORE_SEQ_START:
return int(str(pe) + str(pe + dist) + str(pe + (2 * dist)))
def problem51(nr_prime_family):
"""Problem 51 - Prime digit replacements"""
for p in pelib.primes_sieve(LIMIT):
bool_res, mask, matching_vals = check_digit_replacment(p, nr_prime_family)
if bool_res:
# Return first value of family
return replace_numbers_on_mask(list(str(p)), mask, str(matching_vals[0]))
def problem35(limit):
"""Problem 35 - Circular primes"""
result = 0
for p in pelib.primes_sieve(limit):
if is_circular_primes(p):
result += 1
return result
def check_goldbach(n):
if pelib.is_prime(n):
return True
for p in pelib.primes_sieve(n):
np2 = (n - p) / 2
np2_root = math.sqrt(np2)
if np2_root == int(np2_root):
return True
return False
def check_property(n_str):
p_gen = pelib.primes_sieve(20)
property_holds = True
for i in range(1, len(n_str) - 3 + 1):
p = next(p_gen)
n = int(n_str[i:i + 3])
if n % p != 0:
property_holds = False
break
return property_holds
def problem37():
"""Problem 37 - Truncatable primes"""
result = 0
nrTruncPrimes = 0
for p in pelib.primes_sieve(LIMIT):
if isTruncatablePrime(p):
nrTruncPrimes += 1
result += p
return result