def main2():
s = 0
n = 953
i = 0
m = 0
primes = sieve(47618)
for i in range(len(primes)):
s += primes[i]
if s > 999999:
break
if isprime(s):
print(s)
n = s
m = i + 1
else:
for j in range(i):
if i + 1 - j < m:
break
s -= primes[j]
if isprime(s):
n = s
m = i - j
break
return n
def max_consecutive(primes):
for i in reversed(range(len(primes))):
for j in reversed(range(len(primes)-i+1)):
total=sum(primes[j:j+i])
if isprime(total) and total<1000000:
return total, j, i
return False
def max_consecutive(primes):
for i in reversed(range(len(primes))):
for j in reversed(range(len(primes) - i + 1)):
total = sum(primes[j:j + i])
if isprime(total) and total < 1000000:
return total, j, i
return False
def goldbach2(i, lesser_primes):
if isprime(i):
return True
else:
for j in lesser_primes:
base = sqrt((i - j) / 2)
if base == int(base):
return True
return False
def goldbach2(i,lesser_primes):
if isprime(i):
return True
else:
for j in lesser_primes:
base=sqrt((i-j)/2)
if base==int(base):
return True
return False
def euler35(): ans = [] primeset = [i for i in range(2,1000000) if pr.isprime(i)] for i in primeset: if i not in ans: prime = str(i) circprimes = set() iscirc = True for j in range(0, len(prime)): circprime = int(prime[j:] + prime[:j]) circprimes.add(circprime) if not pr.isprime(circprime): iscirc = False break if iscirc: ans.extend(circprimes) print ans print len(ans)
def euler37(): ans = [] starting = 10 while len(ans) < 11: primes = [i for i in range(starting, starting+10000) if pr.isprime(i)] starting += 10000 for prime in primes: primestr = (str(prime), str(prime)) trunc = True while len(primestr[0]) > 1: primestr = (primestr[0][1:], primestr[1][:len(primestr[1])-1]) if not (pr.isprime(int(primestr[0])) and pr.isprime(int(primestr[1]))): trunc = False break if trunc: ans.append(prime) print ans print sum(ans)
def main():
l = []
n = '11'
while True:
if n[0] in '2357' and n[-1] in '357' and '0' not in n and isprime(
int(n)):
if len(n) == 2:
l.append(int(n))
else:
for i in range(2, len(n)):
if not isprime(int(n[:i])) or not isprime(int(n[-i:])):
break
else:
l.append(int(n))
if len(l) == 11:
break
n = str(int(n) + 2)
return sum(l)
def testprime(n, primeset, compset): if n in primeset: return True elif n in compset: return False elif ip.isprime(n): primeset.add(n) return True else: compset.add(n) return False
def euler72(): bound = 11+1 ans = 0 tot = dict() tot[4] = 2 primes = [i for i in range(bound) if ip.isprime(i)] for prime in primes: tot[prime] = prime-1 for i in range(2, bound): ans += totient(i, tot) print ans return tot
def largestPrimes(num):
import sys
sys.path.append(
'D:\\Users\\Jesus Chua\\Documents\\GitHub\\ProjectEuler\\CommonLibrary'
)
from isprime import isprime
largestPrimes = []
for i in range(num, 1, -1):
if isprime(i):
largestPrimes.append(i)
if len(largestPrimes) >= 10:
return largestPrimes
return largestPrimes
def euler51():
ansdict = dict()
found = False
winner = ''
for candidate in xrange(10001, 100000000, 2):
if ip.isprime(candidate):
digits = str(candidate)
for digit in set(digits):
pattern = digits.replace(digit, '*')
if pattern not in ansdict:
ansdict[pattern] = [0,[]]
for otherdigit in range(10):
newcandidate = int(pattern.replace('*', str(otherdigit)))
if ip.isprime(newcandidate) and len(str(newcandidate)) == len(str(candidate)):
ansdict[pattern][0] += 1
ansdict[pattern][1].append(int(newcandidate))
if ansdict[pattern][0] == 8:
winner = pattern
found = True
if found == True:
break
print ansdict[winner][1]
print min(ansdict[winner][1])
def main1():
#47619 = 1.000.000 / 21
n = 953
m = 21
primes = sieve(47618)
for j in range(m, 600, 2):
for i in range(len(primes)):
p = sum(primes[i:i + 1 + j])
if isprime(p) and p < 1000000:
print(p)
print(primes[i:i + 1 + j])
#m += 2
n = p
if i + m > len(primes) or p > 999999:
break
print(j)
return n
def main(limit):
n = 0
primes = sieve(limit)
for p in primes:
i = 0
p = str(p)
p2 = p
while isprime(int(p2), primes=primes):
i += 1
if p2 == p[-1] + p[0:-1]:
break
p2 = p2[1:] + p2[0]
if i == len(p):
n += 1
if limit > 10:
n += 1 #because 11 is an exception
return n
def main(alimit, blimit):
"""
If limit = 100, then |a| < 100
"""
longest_seq = (0,0,0) #length, a, b
primes = sieve(1000)
if alimit % 2 == 0:
v = 1
for a in range(-alimit+v, alimit, 2):
for b in primes:
n = 0
while isprime(n**2 + a*n + b):
n += 1
if n > longest_seq[0]:
longest_seq = (n, a, b)
return longest_seq
def primedivs(n):
count = 0
for i in range(1, n + 1):
if isprime(i) == 1:
if n % i == 0:
print i
from isprime import isprime
total = 0
for i in range(2, 2 * 10**6):
if isprime(i):
total += i
print(total)
from isprime import isprime
from itertools import permutations
digits=''.join(map(str, range(1,10)))
primes=[]
for i in reversed(range(1,10)):
for nums in permutations(digits[:i], i):
nums=''.join(nums)
if isprime(int(nums)):
primes.append(int(nums))
if primes:
break
print max(primes)
from isprime import isprime
for i in range (1, 99):
print (i, isprime(i))
import isprime print(isprime.isprime(0)) print(isprime.isprime(2)) print(isprime.isprime(3)) print(isprime.isprime(4)) print(isprime.isprime(91)) print(isprime.isprime(97))
def testNumber(a,n):
if isprime(n):
return True
res = modexp(a, n-1, n)
return res != 1
from isprime import isprime
from math import sqrt
primes=[]
def goldbach2(i,lesser_primes):
if isprime(i):
return True
else:
for j in lesser_primes:
base=sqrt((i-j)/2)
if base==int(base):
return True
return False
flag=True
i=1
while flag:
i+=1
if isprime(i):
primes.append(i)
flag=True
else:
flag=goldbach2(i, primes)
print i
def circular_prime(i):
for idx in range(len(str(i))):
if not isprime(rotation(i,idx)):
return False
return True
from isprime import isprime
from lottery import lottery
print(isprime(91))
print(isprime(97))
lottery_numbers = lottery()
for number in lottery_numbers:
print(number)
print(isprime(number))
from isprime import isprime
n = input('enter a number ')
isprime(n)
from isprime import isprime
for n in range(2,20):
print(n, ' is ', isprime(n))
import isprime
print(isprime.isprime(7))
print(isprime.isprime(8))
print(isprime.isprime(91))
print(isprime.isprime(97))
z = int(input("enter any integer: "))
res = isprime.isprime(z)
if res == True:
print(str(z) + " is prime")
else:
print(str(z) + " is not prime")
print(res)
def main():
for n in permutations('7654321', 7):
if isprime(int(''.join(n))):
return ''.join(n)
def primedivs(n): count=0 for i in range(1,n+1): if(isprime(i)==1): if(n%i==0): print i
from isprime import isprime
best=(0,0)
nmax=0
for a in range(-999,1000):
for b in range(-999,1000):
n=0
while isprime(n**2+a*n+b):
n+=1
if n > nmax:
nmax=n
best=(a,b)
print 'new n is', n
print 'new pair is', best
print 'best n is', nmax
print 'best pair is', best
print 'best product is', best[0]*best[1]
def iscatprime(a,b): return ip.isprime(int(str(a) + str(b))) and ip.isprime(int(str(b) + str(a)))
from isprime import isprime
n=input('enter a number ')
isprime(n)
