def run():
primes = primelist(1000000)[4:]
truncPrimes = []
for p in primes:
if all(is_prime(x) for x in leftTrunc(p)) and all(is_prime(x) for x in rightTrunc(p)):
truncPrimes.append(p)
if len(truncPrimes) == 11:
break
return sum(truncPrimes)
def checkforAppendablePrimes(
thisSet, depth,
maxDepth): #recursive function checking appendable primality
for q in (q for q in primes if q > thisSet[-1]):
qIsCandidate = True
for x in thisSet:
if not (is_prime(int(str(x) + str(q)))
and is_prime(int(str(q) + str(x)))):
qIsCandidate = False
if qIsCandidate:
if depth == maxDepth - 1:
return thisSet + [q]
furtherTesting = checkforAppendablePrimes(thisSet + [q], depth + 1,
maxDepth)
if furtherTesting != [0]:
return furtherTesting
return [0]
def run():
N = 1000000
primes = primelist(N)
circPrimes = []
for i in primes:
if all(is_prime(x) for x in CircPerms(i)):
circPrimes.append(i)
return len(circPrimes)
def run():
for i in range(10, 2, -1):
panlist = []
digits = list(x for x in range(1, i))
perms = list(itertools.permutations(digits))
for p in perms:
temp = int(''.join(map(str, p)))
if all([temp % 2, temp % 3]):
panlist.append(temp)
panlist = list(reversed(sorted(panlist)))
for num in panlist:
if is_prime(num):
return num
return -1
def run():
primes = [x for x in primelist(10000) if numDigits(x) == 4]
for p in primes:
primePerms = list(set(sorted(x for x in Perms(p) if is_prime(x))))
while len(primePerms) >= 3:
diff = primePerms[1] - primePerms[0]
for n in primePerms[2:]:
if (n - primePerms[0]) / diff == 2:
out = ''.join([str(x) for x in primePerms[0:3]])
if len(out) == 12:
return int(out)
primePerms.remove(primePerms[1])
return -1
def run():
cur = 1
cornPrimes = 0
corners = 1
for i in range(1, 30000):
for k in range(1, 4):
cur += 2 * i
if is_prime(cur):
cornPrimes += 1
corners += 1
cur += 2 * i #Don't bother checking the last one because it isnt prime
corners += 1
if cornPrimes / corners < 0.1:
return i * 2 + 1