"""Project Euler problem 27"""
from euler import get_plist
class Answer:
def __init__(self):
self.a = 0
self.b = 0
def setval(self, a,b):
self.a = a
self.b = b
def get(self):
return self.a*self.b
def quad(n, a, b):
return n*n + a*n + b
longest = 0
ans = Answer()
primes = set(get_plist(100000))
for a in range(-1000, 1001):
if a%2==0: continue
for b in range(-1000, 1001):
if not abs(b) in primes: continue
n = 0
while quad(n, a, b) in primes:
n += 1
if n > longest:
longest = n
ans.setval(a,b)
print("Answer: " + str(ans.get()))
# -*- coding:utf-8 -*-
"""Project Euler problem 46"""
from euler import get_plist, is_prime
mx = 10**6
primes = set(get_plist(mx))
ans = 0
for odd in range(9, mx, 2):
if is_prime(odd, primes):
continue
flg = True
for j in [i * i * 2 for i in range(int((mx**0.5) / 2) + 1)]:
if j >= odd: break
if is_prime(odd - j, primes):
flg = False
break
if flg:
ans = odd
break
print("Answer: " + str(ans))
# -*- coding:utf-8 -*-
"""Project Euler problem 10"""
from euler import get_plist
sm = 0
primes = get_plist(2000000)
for i in primes:
sm += i
print("Answer: " + str(sm))
# -*- coding:utf-8 -*-
"""Project Euler problem 7"""
from euler import get_plist
target = 10000
l = 10**6
while True:
primes = get_plist(l)
if len(primes)>=target: break
print("Answer: " + str(primes[target]))
# -*- coding:utf-8 -*-
"""Project Euler problem 51"""
from euler import get_plist
primes = get_plist(10**6)
primesset = set(primes)
avail = []
for prime in primes:
s = [int(d) for d in str(prime)]
for i in range(10):
if s.count(i) == 3:
avail.append((prime, i))
for p in avail:
c = 0
for i in range(10):
t = str(p[0]).replace(str(p[1]), str(i))
if str(int(t))!=t:
continue
if int(t) in primesset:
c+=1
if c==8:
print("Answer: " + str(p[0]))
quit()
# -*- coding:utf-8 -*-
"""Project Euler problem 37"""
from euler import get_plist
primes = get_plist(1000000)
primesset = set(primes)
sm = 0
for p in primes:
if p<10: continue
for i in range(len(str(p))):
if not int(str(p)[i:]) in primesset:
break
else:
for i in range(len(str(p))-1):
if not int(str(p)[:-i-1]) in primesset:
break
else:
sm += p
print("Answer: " + str(sm))
from euler import get_plist
def getPrimeFactor(x, primes):
pf = []
mx = x/2+1
for i in primes:
if mx<i:
break
if x!=1:
if x%i==0:
x/=i
pf.append(i)
return pf
mx = 10**6
primes = get_plist(mx)
chk = 4
fst = 0
cnt = 0
for i in range(mx):
pf = set(getPrimeFactor(i, primes))
if len(pf)==chk:
if cnt==0:
fst = i
cnt += 1
if cnt==chk:
break
else:
cnt = 0
print("Answer: " + str(fst))
# -*- coding:utf-8 -*-
"""Project Euler problem 49"""
from itertools import permutations as p
from euler import get_plist
primes = set(get_plist(10000))
for i in range(1000, 10000):
if i == 1487: continue
fst = i
snd = fst + 3330
thd = snd + 3330
if not fst in primes or not snd in primes or not thd in primes:
continue
pat = set(["".join(ls) for ls in p(str(fst))])
if str(snd) in pat and str(thd) in pat:
break
print("Answer: " + str(fst) + str(snd) + str(thd))
# -*- coding: utf-8 -*-
"""Project Euler problem 243"""
from fractions import Fraction as frac
from itertools import count
from euler import get_plist
def R(d):
return phi(d) / (d - 1)
primes = get_plist(100)
target = frac(15499, 94744)
d = 1
phi = 1
for idx, p in enumerate(primes):
d *= p
phi *= p - 1
if frac(phi, d) < target: break
for i in count(1):
if frac(phi * i, d * i - 1) < target:
break
print("Answer: " + str(d * i))
# -*- coding:utf-8 -*-
"""Project Euler problem 50"""
from euler import get_plist
target = 10**6
primes = get_plist(target)
primesset = set(primes)
mx, ans = 0, 0
for l in range(len(primes)):
for r in range(l+1,len(primes)):
sm = sum(primes[l:r+1])
if sm>target: break
length = (r+1)-l
if sm in primesset and mx<length:
ans = sm
mx = length
print("Answer: " + str(ans))
# -*- coding:utf-8 -*-
"""Project Euler problem 41"""
from euler import get_plist
from itertools import permutations
primes = set(get_plist(7654321))
for pat in reversed(
sorted([
int("".join(l)) for l in list(permutations([x for x in "1234567"]))
])):
if pat in primes:
print("Answer: " + str(pat))
break
else:
for pat in reversed(
sorted([
int("".join(l))
for l in list(permutations([x for x in "1234"]))
])):
if pat in primes:
print("Answer: " + str(pat))
break
# -*- coding:utf-8 -*-
"""Project Euler problem 51"""
from euler import get_plist
primes = get_plist(10**6)
primesset = set(primes)
avail = []
for prime in primes:
s = [int(d) for d in str(prime)]
for i in range(10):
if s.count(i) == 3:
avail.append((prime, i))
for p in avail:
c = 0
for i in range(10):
t = str(p[0]).replace(str(p[1]), str(i))
if str(int(t)) != t:
continue
if int(t) in primesset:
c += 1
if c == 8:
print("Answer: " + str(p[0]))
quit()
# -*- coding:utf-8 -*-
"""Project Euler problem 7"""
from euler import get_plist
target = 10000
l = 10**6
while True:
primes = get_plist(l)
if len(primes) >= target: break
print("Answer: " + str(primes[target]))
# -*- coding:utf-8 -*-
"""Project Euler problem 46"""
from euler import get_plist, is_prime
mx = 10**6
primes = set(get_plist(mx))
ans = 0
for odd in range(9, mx, 2):
if is_prime(odd, primes):
continue
flg = True
for j in [i*i*2 for i in range(int((mx**0.5)/2)+1)]:
if j>=odd: break
if is_prime(odd-j, primes):
flg = False
break
if flg:
ans = odd
break
print("Answer: " + str(ans))
def getPrimeFactor(x, primes):
pf = []
mx = x / 2 + 1
for i in primes:
if mx < i:
break
if x != 1:
if x % i == 0:
x /= i
pf.append(i)
return pf
mx = 10**6
primes = get_plist(mx)
chk = 4
fst = 0
cnt = 0
for i in range(mx):
pf = set(getPrimeFactor(i, primes))
if len(pf) == chk:
if cnt == 0:
fst = i
cnt += 1
if cnt == chk:
break
else:
cnt = 0
print("Answer: " + str(fst))
# -*- coding:utf-8 -*-
"""Project Euler problem 10"""
from euler import get_plist
sm = 0
primes = get_plist(2000000)
for i in primes:
sm += i
print("Answer: " + str(sm))