def sol():
'''
Solution to project euler problem.
'''
def rotate(string, n):
'''
Returns rotated string, shifted by n positions
'''
return string[n:] + string[:n]
def isCircular(n):
'''
Returns true if all permutations of a given prime are also prime.
'''
a = []
for i in range(len(str(n))):
a.append(int(rotate(str(n), i)))
for val in a:
if not pe.isPrime(val):
return False
return True
primes = [n for n in range(2, 1000000) if pe.isPrime(n)]
circular_values = [i for i in primes if isCircular(i)]
return len(circular_values)
def sol():
'''
Solution to project euler problem.
'''
def find_cycle(d):
'''
Return the length of the repeating portion of the decimal
representation of 1/d where d is a positive integer.
'''
remainder = 10
i = 0
while remainder != 10 or i < 1:
remainder = (remainder % d) * 10
i += 1
return i
longest_cycle = 0
current_cycle = 0
max_d = 0
sample_set = [
i for i in range(2, 1000)
if i % 2 != 0 and i % 5 != 0 and pe.isPrime(i)
]
for i in sample_set:
current_cycle = find_cycle(i)
if current_cycle > longest_cycle:
longest_cycle = current_cycle
max_d = i
return max_d
def sol():
'''
Solution to project euler problem.
'''
sum = 0
for i in range(2000000):
if pe.isPrime(i):
sum += i
return (sum)
def count_consecutive_primes(a, b):
'''
Finds the number of consecutive primes generated by
y = n^2 + an + b.
'''
fx = 0
for n in range(100000):
fx = n * n + a * n + b
if not pe.isPrime(fx):
return n
def sol():
'''
Solution to project euler problem.
'''
prime_divisors = []
distinct_primes = []
for i in range(134000, 135000):
prime_divisors = [d for d in pe.divisors(i) if pe.isPrime(d)]
if len(prime_divisors) == 4:
distinct_primes.append(i)
return distinct_primes
def isCircular(n):
'''
Returns true if all permutations of a given prime are also prime.
'''
a = []
for i in range(len(str(n))):
a.append(int(rotate(str(n), i)))
for val in a:
if not pe.isPrime(val):
return False
return True
def isTruncable(n):
'''
Returns if prime is truncable.
'''
truncated_vals = []
a = str(n)
for i in range(len(a)):
truncated_vals.append(int(a[i:]))
truncated_vals.append(int(a[:i+1]))
for n in truncated_vals:
if not pe.isPrime(n):
return False
return True
def sol():
'''
Solution to project euler problem.
'''
primes = [n for n in range(1000000) if pe.isPrime(n)]
temp_sum = 0
sums = []
for i in primes:
temp_sum += i
if temp_sum >= 1000000:
break
sums.append(temp_sum)
return max(sums)
def sol():
'''
Solution to project euler problem.
'''
# Generate permutations of digits 1-9
digits = ['1', '2', '3', '4', '5', '6', '7', '8', '9']
perms = []
perms_digits = []
listprime = []
for i in range(1, 10):
perms = list(itertools.permutations(digits[:i]))
perms_digits = [(int(''.join(j))) for j in perms]
listprime += perms_digits
return max([num for num in listprime if pe.isPrime(num)])
def sol():
'''
Solution to project euler problem.
'''
primes = [i for i in range(1488, 10000) if pe.isPrime(i)]
STEP = 3330
for n in primes:
perms = list(itertools.permutations(str(n)))
int_perms = []
for i in perms:
res = ''
for g in i:
res += g
int_perms.append(int(res))
if n + STEP in int_perms and n + 2 * STEP in int_perms and n + STEP in primes and n + 2 * STEP in primes:
return str(n) + str(n + STEP) + str(n + 2 * STEP)
def sol():
'''
Solution to project euler problem.
'''
def isTruncable(n):
'''
Returns if prime is truncable.
'''
truncated_vals = []
a = str(n)
for i in range(len(a)):
truncated_vals.append(int(a[i:]))
truncated_vals.append(int(a[:i+1]))
for n in truncated_vals:
if not pe.isPrime(n):
return False
return True
primes = [n for n in range(11,1000000) if pe.isPrime(n)]
trunc_primes = [s for s in primes if isTruncable(s)]
return sum(trunc_primes)