def findPrimePowerTriples():
P_set = set()
for p in primeCheckII.primes(2, -1):
for q in primeCheckII.primes(2, -1):
for r in primeCheckII.primes(2, -1):
val = p**2 + q**3 + r**4
if val < MAX_VAL:
P_set |= {val}
else:
break_q = (r == 2)
break_p = break_q and (q == 2)
break
if break_q:
break
if break_p:
return (P_set)
def findSums(N, n_0, count_self=True):
if count_self and PC.PrimeCheck(N) and N <= n_0:
yield (1)
for n in PC.primes(2, n_0 + 1):
dn = N - n
if dn > 1:
yield (sum([s for s in findSums(dn, min([dn, n]))]))
def primePairSets(a_0,p_dict ):
for a in primeCheckII.primes(a_0):
print(a)
ab_list = []
for i_b in range(len(p_dict)):
b = p_dict[i_b]
if combinePrimes(b,a):
ab_list.append(b)
while len(ab_list) > 3:
b = ab_list.pop(0)
print("\t",b)
bc_list = []
for c in ab_list:
if combinePrimes(b,c):
bc_list.append(c)
while len(bc_list) > 2:
c = bc_list.pop(0)
print("\t\t",c)
cd_list = []
for d in bc_list:
if combinePrimes(c,d):
cd_list.append(d)
while len(cd_list) > 1:
d = cd_list.pop(0)
print("\t\t\t",d)
for e in cd_list:
if combinePrimes(d,e):
return([b,c,d,e,a])
p_dict[len(p_dict)] = a
def isSquarefree(x):
if x == 1:
return (True)
for p in primeCheckII.primes():
p2 = p**2
if p2 > x:
return (True)
elif x % p2 == 0:
return (False)
def getFactors(x):
X = x
#factor_list = []
while True:
success = False
max_p = int(sqrt(X))
for p in primes(2, max_p + 1):
if X % p == 0:
success = True
X /= p
yield (p)
break
if not success:
yield (int(X))
break
def findSpecialPrimes():
checked_list = []
for prime in primeCheckII.primes(1000,10000):
#print(prime)
for p in permutation([x for x in range(len(str(prime)))],len(str(prime))):
s = [str(prime)[x] for x in p]
next_prime = int("".join(s))
if len(str(next_prime)) < PRIME_LENGTH or next_prime <= prime:
continue
if primeCheckII.PrimeCheck(next_prime):
d_prime = next_prime - prime
last_prime = next_prime + d_prime
if len(str(last_prime)) != PRIME_LENGTH:
continue
if primeCheckII.PrimeCheck(last_prime):
if Counter([s for s in str(last_prime)]) == Counter(s):
if prime not in checked_list:
checked_list.append(prime)
yield([prime,next_prime,last_prime])
def findPrimeFactors(x, n):
prime_factors = {}
X = x
for p in primeCheckII.primes():
if p > X:
break
while X % p == 0:
X /= p
if p not in prime_factors:
prime_factors[p] = 1
else:
prime_factors[p] += 1
if len(prime_factors) > n:
return (False)
if X == 1:
break
if len(prime_factors) != n:
return (False)
#print(x,prime_factors)
return (prime_factors)
Nstart = 5
Nend = 10000
SumD = 0
K = 1
K_list = []
for N in range(Nstart, Nend + 1):
result = K
for k in range(K, N):
Q = ((k / (k + 1))**k) * (N / (k + 1))
if Q < 1:
result = k
break
if result > K:
K = result
K_list = [
x for x in getFactors(K)
if x in [p for p in primes(3, K + 1) if p != 5]
]
D = -N
M = N
for factor in K_list:
if M % factor != 0:
D = N
break
else:
M /= factor
#print(N,K,D,K_list)
SumD += D
print(SumD)
]
new_list += val_list
p += 1
x = X**p
for item in new_list:
yield (item)
def computeValue(numList):
val = 1
for num in numList:
val *= num
return (val)
prime_list = [p for p in primes(2, 30)]
number_list = [2]
total_divisors = 1000
try_list = [number_list]
k = 0
result = []
while True:
#print([[computeValue(i),len([x for x in generateDivisors(i)]),i] for i in try_list])
tried_list = []
for attempt in try_list:
skip_attempt = False
# PROJECT EULER PROBLEM 60 - Prime Pair Sets
import permutations
import primeCheckII
from memoise import Memoise
@Memoise
def combinePrimes(a,b):
return(primeCheckII.PrimeCheck(int(str(a)+str(b))) and primeCheckII.PrimeCheck(int(str(b)+str(a))))
UNIQUE_PRIMES = 5
MIN_SUM = 792
p_dict = {x: p for x,p in enumerate(primeCheckII.primes(3,673))}
def primePairSets(a_0,p_dict ):
for a in primeCheckII.primes(a_0):
print(a)
ab_list = []
for i_b in range(len(p_dict)):
b = p_dict[i_b]
if combinePrimes(b,a):
ab_list.append(b)
while len(ab_list) > 3:
b = ab_list.pop(0)
print("\t",b)
bc_list = []
for c in ab_list:
if combinePrimes(b,c):
bc_list.append(c)
while len(bc_list) > 2:
c = bc_list.pop(0)
# PROJECT EULER PROBLEM 7 - 10001st Prime
from primeCheckII import primes
count = 1
max_count = 10001
for p in primes():
if count == max_count:
print(p)
break
count += 1
def _rotPrime(str_p):
new_str_p = str_p[1:] + str_p[0]
p_list = [int(str_p)]
while new_str_p != str_p:
if not primeCheckII.PrimeCheck(int(new_str_p)):
return (False)
p_list.append(int(new_str_p))
new_str_p = new_str_p[1:] + new_str_p[0]
return (p_list)
BAD_NUMS = ['2', '4', '5', '6', '8', '0']
circ_primes = []
for p in primeCheckII.primes(2, 1000000):
if p in circ_primes:
continue
str_p = str(p)
if len(str_p) == 1:
circ_primes.append(p)
else:
if not any([b in str_p for b in BAD_NUMS]):
rot_primes = _rotPrime(str_p)
if rot_primes:
for val in rot_primes:
if val not in circ_primes:
circ_primes.append(val)
print(rot_primes)
print(circ_primes)
# PROJECT EULER PROBLEM 10 - Summation of Primes
from primeCheckII import primes
max_prime = 2000000
total = 0
for p in primes(2, max_prime):
total += p
print(total)
# PROJECT EULER PROBLEM 46 - Goldbach's Other Conjecture
from math import sqrt
import primeCheckII
def oddComposite():
x = 9
yield(x)
while True:
x += 2
if primeCheckII.PrimeCheck(x):
continue
yield(x)
for x in oddComposite():
if not any([sqrt((x-p)//2)%1==0 for p in primeCheckII.primes(3,x)]):
print(x)
break
#print(x)
# PROJECT EULER PROBLEM 43 - Sub-string Divisibility
from primeCheckII import primes
from permutations import permutation
GOOD3 = [0, 2, 4, 6, 8]
GOOD5 = [0, 5]
prime_list = [p for p in primes(2, 18)]
results = []
for digit3 in GOOD3:
digit_list = [x for x in range(10)]
new_num = ['X' for x in range(10)]
new_num[3] = digit3
digit_list.remove(digit3)
for digit5 in GOOD5:
new_digit_list = digit_list[:]
if digit3 == digit5:
continue
new_num[5] = digit5
new_digit_list.remove(digit5)
for p in permutation(new_digit_list, len(new_digit_list)):
num = ''
for d in new_num:
if d == 'X':
num += str(p.pop(0))
else:
num += str(d)
good_num = True