def run():
thres = int(10**10)
for _n, p in enumerate(primelist(1000000)):
n = _n + 1
if n % 2 == 0:
continue
elif 2 * n * p > thres:
return n
def run():
n = 1000000
primes = primelist(n)
i, result = 0, 1
while result * primes[i] < n:
result *= primes[i]
i += 1
return result
def run():
N = 1000000
primes = primelist(N)
circPrimes = []
for i in primes:
if all(is_prime(x) for x in CircPerms(i)):
circPrimes.append(i)
return len(circPrimes)
def run():
primes = primelist(10000000)
Asmall, _ = sequence_slow(80, primes)
Abig = sequence_fast(500500-80, Asmall, primes)
out = 1
for i, a in enumerate(Abig):
out = (out*primes[i]**(2**a-1)) % 500500507
return out
def primeFactors(x):
# returns the prime factors of x.
primes = primelist(x + 1)
factors = []
while x > 1:
for p in primes:
if x % p == 0:
factors.append(p)
x = x // p
break
return factors
def run():
primes = primelist(1000000)[4:]
truncPrimes = []
for p in primes:
if all(is_prime(x) for x in leftTrunc(p)) and all(is_prime(x) for x in rightTrunc(p)):
truncPrimes.append(p)
if len(truncPrimes) == 11:
break
return sum(truncPrimes)
def run():
p_max = 1000000
a_max = int(sqrt(p_max - 1))
primes = primelist(p_max)
ans = {}
for a in range(1, a_max):
p = 3 * a**2 + 3 * a + 1
if p in primes:
ans[p] = a
#for k, v in ans.items(): print(f'p = {k}, n = {v}')
return len(ans)
def run(N=10000000):
primes = primelist(N // 2)
Sum = 0
for i, p in enumerate(primes):
if p * primes[i + 1] > N:
break
for q in primes[i + 1:]:
if p * q > N: break
M = largest_integer_divisible_by_2_primes(p, q, N)
#print(p, q, M)
Sum += M
return Sum
def run():
target = 8
primes = primelist(1000000)
found = False
targetExclusionList = ''
targetRepDigs = ''
for n in range(2, 8):
primeSet = list((str(x)) for x in primes if numDigits(x) == n)
for ex in exclusionList(n):
currentCount = Counter()
for p in primeSet:
repDigs = ''
changeDigs = ''
for i, k in enumerate(ex):
if k == '1': #exclude
changeDigs += p[i]
else:
repDigs += p[i]
if changeDigs.count(changeDigs[0]) == len(
changeDigs): #if all changing digits are equal
currentCount[repDigs] += 1
if currentCount[repDigs] == target:
found = True
targetExclusionList = ex
targetRepDigs = repDigs
if found:
break
if found:
break
if found: #go through array again and print answers
ans = []
for p in primeSet:
repDigs = ''
changeDigs = ''
for i, k in enumerate(targetExclusionList):
if k == '1': #exclude
changeDigs += p[i]
else:
repDigs += p[i]
if changeDigs.count(changeDigs[0]) == len(
changeDigs): #if all changing digits are equal
if repDigs == targetRepDigs:
ans.append(p)
break
return min(int(x) for x in ans)
def run():
primes = [x for x in primelist(10000) if numDigits(x) == 4]
for p in primes:
primePerms = list(set(sorted(x for x in Perms(p) if is_prime(x))))
while len(primePerms) >= 3:
diff = primePerms[1] - primePerms[0]
for n in primePerms[2:]:
if (n - primePerms[0]) / diff == 2:
out = ''.join([str(x) for x in primePerms[0:3]])
if len(out) == 12:
return int(out)
primePerms.remove(primePerms[1])
return -1
def run():
N = 50000000
primes = primelist(N)
count = 2
for p in primes[1:]:
if (p+1)%4 == 0:
# print(p)
count += 1
if (2*p+2)%4 == 0 and 4*p < N:
# print(4*p)
count += 1
if (4*p+4)%4 == 0 and 16*p < N:
# print(16*p)
count += 1
return count
def run():
primes = primelist(10000)
squares = list(x * x for x in range(1, 100))
for i in range(7, 10000, 2):
if i not in primes:
thisNumisGood = False
for p in (x for x in primes if x <= i - 1):
if ((i - p) / 2).is_integer() and int((i - p) / 2) in squares:
thisNumisGood = True
if not thisNumisGood:
return i
break
return -1
def run():
primes = primelist(limit)
aMax, bMax, nMax = 0, 0, 0
for a in range(-Range, Range):
# b must be prime for the case n=0
for b in (b_ for b_ in primes if b_ < Range):
f = lambda x: x**2 + a * x + b
n = 0
while f(n) in primes:
n += 1
if n > nMax:
aMax, bMax, nMax = a, b, n
return aMax * bMax
def run():
primes = primelist(100)
for n in range(2, 100):
num_ways = ways(n, len(primes) - 1, primes)
if num_ways > 5000:
return n
# -*- coding: utf-8 -*-
"""
Solution to Project Euler problem 110
Author: Jaime Liew
https://github.com/jaimeliew1/Project_Euler_Solutions
"""
from EulerFunctions import primelist
from collections import Counter
from math import sqrt, ceil
N_max = int(5e8)
primes = primelist(N_max)
def product(lst):
out = 1
for x in lst:
out *= x
return out
def primeFactor(n):
primefactors = Counter()
while n > 1:
for p in primes:
if n%p == 0:
n = n//p
primefactors[p] += 1
return dict(primefactors)
def run():
N = 600851475143
return max(p for p in primelist(int(N**0.5)) if N % p == 0)
# -*- coding: utf-8 -*-
"""
Solution to Project Euler problem X
Author: Jaime Liew
https://github.com/jaimeliew1/Project_Euler_Solutions
"""
from EulerFunctions import primelist
primes = primelist(100000)
def npf(n): #number of prime factors
num = 0
for p in (x for x in primes if x <= n / 2):
if n % p == 0:
num += 1
if num == 0:
return 1
else:
return num
def run():
notFound = True
i = 134000 # 2*3*5*7
while notFound:
if i % 1000 == 0:
#print(i)
def run():
N = 2000000
primes = primelist(N)
return sum(primes)
return -1
