import primecache
limit = 1000000
prime_list = primecache.primelist(limit)
prime_sum = [0] * (len(prime_list) + 1)
prime_sum[0] = 0
for i in range(len(prime_list)):
prime_sum[i + 1] = prime_sum[i] + prime_list[i]
# print(prime_list)
# print(prime_sum)
longest_chain = 0
ans = 0
for i in range(len(prime_sum) - 1, 0, -1):
for j in range(0, i - longest_chain):
chain = 0
if prime_sum[i] - prime_sum[j] < limit and prime_sum[i] - prime_sum[
j] in prime_list:
chain = i - j
# print(prime_sum[i],prime_sum[j],prime_sum[i]-prime_sum[j],chain)
if chain > longest_chain:
longest_chain = chain
ans = prime_sum[i] - prime_sum[j]
break
print(ans, longest_chain)
import primecache
prime_list = primecache.primelist(150000)
def primefactors(num):
pf = []
i = 0
while num > 1:
if num % prime_list[i] == 0:
while num % prime_list[i] == 0:
num /= prime_list[i]
if prime_list[i] in pf or len(
pf) > 0 and pf[len(pf) - 1] % prime_list[i] == 0:
pf[len(pf) - 1] *= prime_list[i]
else:
pf.append(prime_list[i])
i += 1
else:
i += 1
return pf
notfound = True
start = 10
lim = 4
while notfound:
chain = 0
cons_prime = []
cons_prime_len = []
for i in range(start, start + lim):
#composite = prime + 2*square
import primecache
import math
def isSquare(num):
return math.sqrt(num) == int(math.sqrt(num))
plist = primecache.primelist(10000)
clist = []
for p in range(2,10000):
if p not in plist:
clist.append(p)
print(plist)
print(clist)
passnum = []
for c in clist:
check = 0
found = False
for p in plist:
#check = 0
if c>p and isSquare(int((c-p)/2)):
check *= 0
found = True
break
else:
check += 1
if found == True:
passnum.append(c)
print(c,p)
import math, primecache
def isSquare(num):
return math.sqrt(num) == int(math.sqrt(num))
print(primecache.primelist(10**6))
#totient(n) = n(1-1/p1)(1-1/p2)...
import primecache
prime_list = primecache.primelist(600000)
# def primefactors(num):
# pf = []
# while num > 1:
# for p in primes:
# while num%p==0:
# num = num/p
# if p not in pf:
# pf.append(p)
# break
# return pf
def primefactors(num):
pf = []
i = 0
while num>1:
if num%prime_list[i]==0:
while num%prime_list[i]==0:
num/=prime_list[i]
if prime_list[i] not in pf:
pf.append(prime_list[i])
i += 1
else:
i += 1
return pf
def totient(num):
import primecache
p = primecache.primelist(10**5)
def countPrime(nlist):
count = 0
for i in nlist:
if i in p:
count += 1
return count
rounds = 1
numlist = []
numlist.append(1)
while True:
for i in range(1, 5):
numlist.append(numlist[-1] + 2 * rounds)
rounds += 1
#print((rounds-1),(rounds-1)*2+1,numlist,countPrime(numlist),len(numlist),countPrime(numlist)/len(numlist))
if countPrime(numlist) / len(numlist) < 0.1:
break
print((rounds - 1) * 2 + 1)
for i in range(len(str(num))):
ret.append(int(str(num)[i:]))
#ret.append(int(str(num)[:(-1*(i+1))]))
return ret
def truncate_number_r(num):
ret = []
for i in range(len(str(num))):
ret.append(int(str(num)[:len(str(num)) - i]))
#ret.append(int(str(num)[:(-1*(i+1))]))
return ret
sum = 0
primes = primecache.primelist(800000)
for i in primes[4:]:
l = truncate_number(i)
r = truncate_number_r(i)
there_l = 1
for nums in l:
if nums in primes:
there_l *= 1
else:
there_l *= 0
there_r = 1
for nums in r:
if nums in primes:
there_r *= 1
else: