def Prime_div(num,Prime,divisors):
""" Recursively Finds the prime divisors of a given number,
Args:
num (int): Number whose Prive divisors will be calculated
Prime (Prime) : An instance of the Prime class used to generate primes
divisors (list): A list representing the divisors found so far
"""
if divisors == []: #if this is the first call add one to list all numbers div by 1
divisors.append(1)
if Prime.isPrime(num):#base case. when prime number is found we have found all Prime divisors
temp = divisors
divisors.append(num)
return divisors
else:# testing case. If we have not found our base prime, then we keep calling the function
Prime.reset()
factor = Prime.nextPrime()
found = False#Set to false in each call
while factor < num/2 and not found:
if num%factor == 0:
divisors.append(factor)#Appends a found prime divisor to our list
found = True
if not found:
factor = Prime.nextPrime()#Cycles through prime list until we find a prime the number is divisible by
return Prime_div(num/factor,Prime,divisors)
from prime import Prime
longest = 0
ans = 0
Prime.isPrime(1000000)
for i in range(0, len(Prime.p)):
curr = 0
value = 0
for j in range(i, len(Prime.p)):
curr += 1
value += Prime.p[j]
if value > 1000000:
break
if Prime.isPrime(value) and curr > longest:
longest = curr
ans = value
if longest >= curr:
break
print(ans)
from prime import Prime
ans = 0
curr = 0
for b in Prime.prime():
if b > 1000:
break
for a in range(-999, 1000):
n = 0
for i in map(lambda x: b + a * x + x**2, range(2000)):
if not Prime.isPrime(i):
break
n += 1
if n > curr:
curr = n
ans = a * b
print(ans)
m = dict()
ans = 0
def Add(s, t, i, n):
global m
global ans
if len(s) == 0:
return
c = t + 'x' + s[1:]
if i == -1 or int(s[0]) == i:
if c not in m:
m[c] = list()
m[c].append(n)
if len(m[c]) == 8:
ans = m[c][0] if ans == 0 else min(ans, m[c][0])
Add(s[1:], t + 'x', int(s[0]), n)
Add(s[1:], t + s[0], i, n)
i = 0
j = 1
while ans == 0:
i = j
j *= 10
for k in range(i, j):
if Prime.isPrime(k):
Add(str(k), '', -1, k)
print(ans)
from prime import Prime
left = {2, 3, 5, 7}
right = {2, 3, 5, 7}
ans = 0
count = 0
while len(left) != 0 and len(right) != 0 and count < 11:
l = set()
r = set()
for i in left:
for j in range(1, 10):
n = int(str(j) + str(i))
if Prime.isPrime(n):
l.add(n)
for i in right:
for j in range(1, 10):
n = i * 10 + j
if Prime.isPrime(n):
r.add(n)
left = l
right = r
for i in left.intersection(right):
ans += i
count += 1
print(ans)
from prime import Prime
for c in range(3, 9999999999999999999999999999999999999999999, 2):
if Prime.isPrime(c):
continue
for i in map(lambda x: x ** 2 * 2, range(1, 1000000000000000000000000000000000000000000)):
if c < i:
print(c)
exit(0)
if Prime.isPrime(c - i):
break
from prime import Prime
def toKey(n):
return int(''.join(sorted(str(n))))
s = list(map(lambda x: list(), range(10000)))
for i in range(1000, 10000):
if Prime.isPrime(i):
s[toKey(i)].append(i)
for t in s:
for i in range(len(t) - 2):
for j in range(i + 1, len(t) - 1):
if t[j] * 2 - t[i] in t:
if t[i] != 1487 and t[j] != 4817:
print(t[i], t[j], t[j] * 2 - t[i], sep='')
from prime import Prime
ans = 0
for i in range(2, 1000000):
r = str(i)
while i > 0:
if not Prime.isPrime(int(r)):
break
r = str(i%10) + r[:-1]
i //= 10
if i == 0:
ans += 1
print(ans)
