def solve():
print('start')
o = 10
for p in primes.primes_sieve(27000):
if p == 2 or p == 5:
continue
while p > o:
o *= 10
for g in groups:
if ok(g, (p, o)):
newg = list(g)
newg.append((p, o))
groups.append(newg)
if (len(newg)) >= 5:
print(newg, sum(x[0] for x in newg))
from primes import primes_sieve
import itertools
is_prime = primes_sieve(9999)
def check_sequence(a):
prime_set = [
int("".join(x)) for x in itertools.permutations(str(a))
if is_prime[int("".join(x))]
]
l = len(prime_set)
if l >= 3:
for i in range(l):
for j in range(i + 1, l):
for k in range(j + 1, l):
a = prime_set[k] - prime_set[j]
if a == prime_set[j] - prime_set[i] and a > 0:
print prime_set[i], prime_set[j], prime_set[k]
return True
return False
for i in range(1488, 9999):
check_sequence(i)
from primes import primes_sieve, primes_sieve_gen
limit = 1000000
primes = [x for x in primes_sieve_gen(10000)]
is_prime = primes_sieve(1000000)
squares = [i * i for i in range(1, 100)]
first = [i for i in range(2, limit) if not i % 2 == 0 and not is_prime[i]]
second = [False] * limit
for i in first:
second[i] = True
for i in primes:
for j in squares:
second[i + 2 * j] = False
print second.index(True)
def has_at_least_3_same_digits(number):
d = {}
for letter in str(number):
if letter not in d.keys():
d[letter] = 1
else:
d[letter] += 1
return max(d.itervalues()) >= 3
limit = 1000000
primes = [x for x in primes_sieve_gen(limit)]
primes = primes[primes.index(56003) - 1:]
is_prime = primes_sieve(limit)
replacement_digits = (1, 2, 3, 4, 5, 6, 7, 8, 9, 0)
def calculate():
found = False
already_checked = []
counter = 10
while not found:
prime = primes.pop(0)
if not has_at_least_3_same_digits(prime):
continue
print prime
for n_of_digits in xrange(3, len(str(prime)), 3):
for sequence in set(["".join(c) for c in
itertools.combinations('0123456789'[:len(str(prime))-1], n_of_digits)]):
#!/usr/bin/python
import primes
p = list(primes.primes_sieve(10**6))
def isPrime(n):
if n <= 1:
return False
if n % 2 == 0:
return n == 2
for i in xrange(100000):
if p[i] * p[i] > n:
return True
if n % p[i] == 0:
return False
sss = 0
for d in xrange(0, 10):
print d
o = int(str(d) * 10)
if isPrime(o):
sss += o
print o
continue
found = set()
for a in xrange(0, 10):
for pos in xrange(0, 10):
c = [d] * pos + [a] + [d] * (9 - pos)
#!/usr/bin/python3
import primes
p = list(primes.primes_sieve(8000000))
def t(n):
return n*(n+1)//2
assert t(8) == 36
def s(n):
start = t(n - 3) + 1
end = t(n + 2) + 1
m = [1] * (end - start)
neighbours = [0] * (end - start)
s = 0
filterPr(start, end, m, p)
#print(1, sum(1 for x in m if x > 0))
filterNeigh(n, start, end, m, neighbours)
#print(2, sum(1 for x in m if x > 0))
for x in range(t(n - 1) + 1, t(n) + 1):
if m[x - start] >= 2 or (m[x - start] == 1 and m[neighbours[x - start] - start] >= 2):
s += x
return s
def filterPr(start, end, m, pr):
for p in pr:
if p*p > end:
break
#!/usr/bin/python
import primes
import itertools
p = list(primes.primes_sieve(120000))
def factors(n):
if n <= 1:
return []
f = 0
r = []
while p[f] <= n:
isf = False
while n % p[f] == 0:
isf = True
n //= p[f]
if isf: r.append(p[f])
f += 1
return r
def solve(limit, cnt):
a = [True] * (limit + 1)
a[0] = a[1] = False
cnt -= 1
while True:
for i, v in enumerate(a):
if v:
c = factors(i)
break
#print c
#!/usr/bin/python3
import primes
pr = list(primes.primes_sieve(1000))
a = {}
def calc(s, m): # how many ways to get sum s using terms less than or equal to m
if s < 0 or s == 1:
return 0
if s == 0:
return 1
if (s,m) in a:
return a[(s,m)]
else:
t = 0
for p in pr:
if p > m or p > s:
break
t += calc(s - p, p)
a[(s,m)] = t
return a[(s, m)]
assert calc(10, 10) == 5
n = 2
while calc(n, n) <= 5000:
n += 1
print(n)
assert n == 71