def spiral_primes():
lCount = 0
lSide = 3
while (True):
lInt = lSide ** 2
lSideM1 = lSide - 1
if utils.is_prime(lInt - lSideM1):
lCount += 1
if utils.is_prime(lInt - lSideM1 * 2):
lCount += 1
if utils.is_prime(lInt - lSideM1 * 3):
lCount += 1
lRatio = lCount / (lSide * 2 - 1)
# print('Side: ' + str(i) + ' Primes: ' + str(lCount) + ' Total: '
# + str(i * 2 - 1) + ' Ratio: '
# + str(lRatio))
if lRatio < 0.1:
return lSide
lSide += 2
def quadratic_primes(pInt):
lSieve = sieve_eratosthenes(pInt, pInt)
lPrimes = []
for i in range(1, pInt):
if lSieve[i] == 1:
lPrimes.append(i)
lMaxNumPrime = 0
lMaxA = 0
lMaxB = 0
for b in lPrimes:
for a in range(-pInt, pInt + 1):
lCurrNumPrime = 0
lN = 0
while is_prime(lN * lN + a * lN + b):
lCurrNumPrime += 1
lN += 1
if lCurrNumPrime > lMaxNumPrime:
lMaxNumPrime = lCurrNumPrime
lMaxA = a
lMaxB = b
return(lMaxA, lMaxB, lMaxNumPrime)
def pandigital_prime():
for i in list(itertools.permutations([7, 6, 5, 4, 3, 2, 1], 7)):
lStr = ''
for j in i:
lStr += str(j)
lInt = int(lStr)
if is_prime(lInt):
return lInt
return None
def main():
"""
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10 001st prime number?
"""
limit = 10001
n = 2
i = 0
while True:
if is_prime(n):
i += 1
if i == limit:
break
if n == 2:
n += 1
else:
n += 2
return n
def main():
"""
https://projecteuler.net/problem=46
"""
primes = [2]
n = 1
while True:
n += 2
if is_prime(n):
primes.append(n)
continue
is_bad = True
for p in primes:
q = ((n - p) / 2)**0.5
if q.is_integer():
is_bad = False
break
if is_bad:
return n
def prime_pair_sets():
lMaxT = 10 ** 6
lSieve = sieve_eratosthenes(lMaxT, lMaxT)
lPrimes = []
lMaxP = 10 ** 4
for i in range(1, lMaxT):
if lSieve[i] == 1:
lPrimes.append(i)
if i < lMaxP:
lMaxPrime = i
lMaxI = lPrimes.index(lMaxPrime) + 1
lInts = np.empty(5, dtype='S10')
for i1 in range(0, lMaxI - 4):
lPrime1 = lPrimes[i1]
lInts[0] = str(lPrime1)
if lPrime1 == 2:
continue
if lPrime1 == 5:
continue
# print('i1: ' + str(lPrime1))
for i2 in range(i1 + 1, lMaxI - 3):
lPrime2 = lPrimes[i2]
lInts[1] = str(lPrime2)
if lPrime2 == 5:
continue
lInt = int(lInts[0] + lInts[1])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[1] + lInts[0])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
# print('i1: ' + str(lPrime1) + ' i2: ' + str(lPrime2))
for i3 in range(i2 + 1, lMaxI - 2):
lPrime3 = lPrimes[i3]
lInts[2] = str(lPrime3)
if lPrime3 == 5:
continue
lInt = int(lInts[0] + lInts[2])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[2] + lInts[0])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[1] + lInts[2])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[2] + lInts[1])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
# print('i1: ' + str(lPrime1) + ' i2: ' + str(lPrime2)
# + ' i3: ' + str(lPrime3))
for i4 in range(i3 + 1, lMaxI - 1):
lPrime4 = lPrimes[i4]
lInts[3] = str(lPrime4)
lInt = int(lInts[0] + lInts[3])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[3] + lInts[0])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[1] + lInts[3])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[3] + lInts[1])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[2] + lInts[3])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[3] + lInts[2])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
# print('i1: ' + str(lPrime1) + ' i2: ' + str(lPrime2)
# + ' i3: ' + str(lPrime3)
# + ' i4: ' + str(lPrime4))
for i5 in range(i4 + 1, lMaxI):
lPrime5 = lPrimes[i5]
lInts[4] = str(lPrime5)
lInt = int(lInts[0] + lInts[4])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[4] + lInts[0])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[1] + lInts[4])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[4] + lInts[1])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[2] + lInts[4])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[4] + lInts[2])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[3] + lInts[4])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
lInt = int(lInts[4] + lInts[3])
if lInt > lMaxT:
if not is_prime(lInt):
continue
elif lSieve[lInt] == 0:
continue
# print('i1: ' + str(lPrime1) + ' i2: ' + str(lPrime2)
# + ' i3: ' + str(lPrime3)
# + ' i4: ' + str(lPrime4)
# + ' i5: ' + str(lPrime5))
return (lPrime1 + lPrime2 + lPrime3
+ lPrime4 + lPrime5)
return None
