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 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 problem58():
"""Problem 58 - Spiral primes"""
fpc = pelib.FastPrimeChecker()
result = 0
nr_primes = 0
nr_total = 0
diagonal_square_spiral_gen = diagonal_square_spiral()
while True:
value = next(diagonal_square_spiral_gen)
if fpc.is_prime(value):
nr_primes += 1
nr_total += 1
if nr_total % 4 == 1:
# print("Side Length: {} Fraction {}/{} = {}".format((nr_total +
# 1) // 2, nr_primes, nr_total, nr_primes / nr_total))
# Full Square
if (nr_primes / nr_total) < .1 and nr_total > 1: # Exclude "1"-case
# Side Length
return (nr_total + 1) // 2
return result
def test_FPC(self):
fpc = pelib.FastPrimeChecker(1000000000)
self.assertTrue(fpc.is_prime(31627))
self.assertFalse(fpc.is_prime(31623))
#!/usr/bin/env python3
"""Project Euler - Problem 37 Module"""
import pelib
LIMIT = 1000000
FPC = pelib.FastPrimeChecker(LIMIT)
def isTruncatablePrime(number):
result = False
str_number = str(number)
# we already know that number is prime
for i in range(1, len(str_number)):
result = True
l_trunc = int(str_number[i:])
r_trunc = int(str_number[:i])
if not (FPC.is_prime(l_trunc) and FPC.is_prime(r_trunc)):
return False
return result
def problem37():
"""Problem 37 - Truncatable primes"""
result = 0
nrTruncPrimes = 0
for p in pelib.primes_sieve(LIMIT):
if isTruncatablePrime(p):
#!/usr/bin/env python3
"""Project Euler - Problem 35 Module"""
import pelib
FPC = pelib.FastPrimeChecker()
def is_circular_primes(number):
str_number = str(number)
# we already know that number is prime
for i in range(1, len(str_number)):
# shift
shifted = int(str_number[i:] + str_number[:i])
if not FPC.is_prime(shifted):
return False
return True
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 run():
"""Default Run Method"""