def truncatable_primes(digits: Tuple[int] = ()) -> Iterable[int]:
candidate_digits_count = len(digits) + 1
for digit in possible_digits:
candidate_digits = (digit,) + digits
candidate_number = digits_to_number(candidate_digits)
if not prime(candidate_number):
continue
if (candidate_digits_count > 1 and
all(prime(digits_to_number(candidate_digits[:position]))
for position in range(1, candidate_digits_count))):
yield candidate_number
yield from truncatable_primes(candidate_digits)
def formula_test(a,b):
n = 0
while True:
if prime(n**2 + a*n + b):
n += 1
else:
break
return n
def consecutive_quadratic_primes_count(coefficients: Tuple[int, int]) -> int:
linear_coefficient, constant_term = coefficients
def quadratic_formula(n: int) -> int:
return n**2 + linear_coefficient * n + constant_term
for number in count(0):
value = quadratic_formula(number)
if value < 0 or not prime(value):
return number
def primeFactors(n):
result = []
while n > 1:
i = 2
while i <= n:
if not n % i and prime(i):
result.append(i)
n //= i
break
i += 1
return result
def nConsecutif(n, m):
result = 0
while numberOfPrimeFactors(n) == m:
n += 1
result += 1
return result
# ********************************************************************
startTime = time.time()
start = 7*11*13*17
n = start
value = 4
while True:
if not prime(n):
consecutif = nConsecutif(n, value)
if consecutif >= value:
break
n += consecutif + 1
else:
n += 1
print(n)
print(time.time() - startTime)
def answer(limit):
return [x for x in xrange(2,limit) if prime(x) and all([prime(int(y)) for y in rotations(str(x))])]
# length of the square spiral for which the ratio of primes along both diagonals
# first falls below 10%?
from utils import prime
from time import time
# ******************************************************************************
startTime = time()
length = 1
primeTotal = 0
total = 1
ratio = 1
while ratio >= 0.10:
length += 2
total += 4
diagonal = length**2
for n in range(3):
diagonal -= length - 1
if prime(diagonal):
primeTotal += 1
ratio = primeTotal / total
# print(length, primeTotal, total, ratio)
print(length)
print(time() - startTime)
# ********************************************************************
from utils import prime, sortedList
import time
startTime = time.time()
primeList = sortedList([])
primeList.add(2)
squareList = sortedList([])
squareList.addList([1,4])
start = 1 # en fait, 3
n = start
bool = True
while bool:
n += 2
squareList.add(n**2)
squareList.add((n+1)**2)
if prime(n):
primeList.add(n)
else:
bool = conjecture(n)
print("Result :", n)
print(time.time() - startTime)