def p050(N=10**6, lim=4000):
primes = numty.sieve(lim)
primeset = set(primes)
bestprime = 0
bestlen = 0
bestbase = 0
i = 0
while True:
if i + bestlen > len(primes):
logger.error('Limit was too low!')
return
cand = sum(primes[i:i + bestlen])
if cand >= N:
break
j = i + bestlen
while cand < N:
if j >= len(primes):
logger.error('Limit was too low!')
return
cand += primes[j]
j += 1
while j > i + bestlen:
if numty.isprime(cand):
bestprime = cand
bestlen = j - i
bestbase = primes[i]
break
cand -= primes[j - 1]
j -= 1
i += 1
logger.debug((bestlen, primes[bestbase:bestbase + bestlen]))
return bestprime
def p027(N=10**3):
lim = 10 * N
table = set(numty.sieve(lim))
primes = numty.sieve(2 * N + 1)
best = 0
best_ab = (0, 0)
for b in primes:
if b > N:
break
for c in primes:
a = c - b - 1
if a > N:
break
count = 2
while True:
cand = count**2 + a * count + b
if cand < 0:
break
if cand < lim and cand not in table:
break
if cand >= lim and not numty.isprime(cand):
break
count += 1
if count > best:
best_ab = (a, b)
best = count
return best_ab[0] * best_ab[1]
def p050(N=10 ** 6, lim=4000):
primes = numty.sieve(lim)
primeset = set(primes)
bestprime = 0
bestlen = 0
bestbase = 0
i = 0
while True:
if i + bestlen > len(primes):
logger.error("Limit was too low!")
return
cand = sum(primes[i : i + bestlen])
if cand >= N:
break
j = i + bestlen
while cand < N:
if j >= len(primes):
logger.error("Limit was too low!")
return
cand += primes[j]
j += 1
while j > i + bestlen:
if numty.isprime(cand):
bestprime = cand
bestlen = j - i
bestbase = primes[i]
break
cand -= primes[j - 1]
j -= 1
i += 1
logger.debug((bestlen, primes[bestbase : bestbase + bestlen]))
return bestprime
def p027(N = 10**3):
lim = 10*N
table = set(numty.sieve(lim))
primes = numty.sieve(2*N+1)
best = 0
best_ab = (0,0)
for b in primes:
if b > N:
break
for c in primes:
a = c - b - 1
if a > N:
break
count = 2
while True:
cand = count**2+a*count+b
if cand < 0:
break
if cand < lim and cand not in table:
break
if cand >= lim and not numty.isprime(cand):
break
count += 1
if count > best:
best_ab = (a,b)
best = count
return best_ab[0]*best_ab[1]
def p058(target=0.1):
primecount = 0
n = 1
while True:
corners = [(2 * n - 1) ** 2 + 2 * n, (2 * n - 1) ** 2 + 4 * n, (2 * n - 1) ** 2 + 6 * n]
primecount += sum(1 for corner in corners if numty.isprime(corner))
if 1.0 * primecount / (4 * n + 1) < target:
return 2 * n + 1
n += 1
def p058(target=0.1):
primecount = 0
n = 1
while True:
corners = [(2 * n - 1)**2 + 2 * n, (2 * n - 1)**2 + 4 * n,
(2 * n - 1)**2 + 6 * n]
primecount += sum(1 for corner in corners if numty.isprime(corner))
if 1.0 * primecount / (4 * n + 1) < target:
return 2 * n + 1
n += 1
def gengraph(N):
primes = numty.sieve(N)
graph = defaultdict(list)
for i in xrange(len(primes)):
p = primes[i]
for j in xrange(i):
q = primes[j]
if (p+q)%3 == 0:
continue
pq = int(str(p)+str(q))
qp = int(str(q)+str(p))
if numty.isprime(pq) and utils.isprime(qp):
graph[p].append(q)
graph[q].append(p)
return graph
def p037():
primes = [2,3,5,7]
allprimes = []
while primes:
logger.debug(primes)
newprimes = []
for prime in primes:
for d in [1,3,7,9]:
if numty.isprime(10*prime+d):
newprimes.append(10*prime+d)
primes = newprimes
allprimes += primes
acc = 0
count = 0
for prime in allprimes:
if truncatable(prime):
logger.debug(prime)
count += 1
acc += prime
logger.debug(count)
return acc
def p041():
for N in range(8,0,-1):
for p in itertools.permutations(range(N,0,-1)):
n = sum(d*10**(len(p)-1-i) for (i,d) in enumerate(p))
if numty.isprime(n):
return n
def truncatable(prime):
str_p = str(prime)
for n in range(len(str_p)):
if not numty.isprime(int(str_p[n:])):
return False
return True