def run():
pr = primes.populatePrimes( 3162 ) #3162 ~= sqrt of (10000000)
def prime(n, primes):
isPrime = True
index = 0
p = primes[index]
limit = int(math.sqrt(n)) + 1
while p < limit:
if n % p == 0:
isPrime = False
break
else:
index += 1
p = primes[ index ]
return isPrime
panPrimes = []
for i in list(itertools.permutations('1234567')):
s = ''
for letter in i:
s += letter
num = int(s)
if num%2 == 0:
continue
else:
if prime(num, pr):
panPrimes.append(num)
return max(panPrimes)
def run():
p = primes.populatePrimes(1000000)
pSet = set(p)
# returns true if first digit is 2, 3 or 7
def firstDigit(n):
first = int(str(n)[0])
return first == 2 or first == 3 or first == 7 or first == 5
# returns true if last digit is 3 or 7
def lastDigit(n):
return n % 10 == 3 or n % 10 == 7
# return true if its prime for all "right truncations"
def rightPrime(n):
if n / 10 == 0 and n in pSet:
return True
else:
trunc = n / 10
return trunc in pSet and rightPrime(trunc)
# return true if its prime for all "left truncations"
def leftPrime(n):
if n / 10 == 0 and n in pSet:
return True
else:
trunc = int(str(n)[1:])
return trunc in pSet and leftPrime(trunc)
count = 0
answers = []
exempt = set([2, 3, 5, 7])
for p in pSet:
if not firstDigit(p) and not lastDigit(p):
continue
else:
if rightPrime(p) and leftPrime(p) and p not in exempt:
count += 1
answers.append(p)
print answers
print sum(answers)
import primes
p4 = [ p for p in primes.populatePrimes(10000) if p/1000 > 1 ]
map = {}
for p in p4:
key = list(str(p))
key.sort()
dkey = reduce(lambda x, y: x + y, key)
if dkey in map:
map[dkey].append(p)
else:
map[dkey] = [p]
count = 0
for k, v in map.iteritems():
v.sort()
for k,v in map.iteritems():
if len(v) >= 3:
if len(v) == 3:
if 2*v[1] == v[0] + v[2]:
print "THE ANSWER!!!!!!!!!!!!!! is %d, %d, %d" %(v[0], v[1], v[2])
else:
found = False
s = {}
for p1 in v:
for p2 in v:
if p1-p2 in s and p1 != p2 and p1 == s[p1-p2][1]:
print "%d, %d. And %d, %d" %(s[p1-p2][0], s[p1-p2][1], p1, p2)
import primes
p = primes.populatePrimes(1000)[3:]
max = (0, 0)
for prime in p:
count = 1
divis = False
while not divis:
#print "We are on prime %d and count %d" %(prime, count)
if ((10**count - 1) % prime) == 0:
divis = True
else:
count += 1
if count > max[1]:
max = (prime, count)
print max
import primes
p4 = [p for p in primes.populatePrimes(10000) if p / 1000 > 1]
map = {}
for p in p4:
key = list(str(p))
key.sort()
dkey = reduce(lambda x, y: x + y, key)
if dkey in map:
map[dkey].append(p)
else:
map[dkey] = [p]
count = 0
for k, v in map.iteritems():
v.sort()
for k, v in map.iteritems():
if len(v) >= 3:
if len(v) == 3:
if 2 * v[1] == v[0] + v[2]:
print "THE ANSWER!!!!!!!!!!!!!! is %d, %d, %d" % (v[0], v[1],
v[2])
else:
found = False
s = {}
for p1 in v:
for p2 in v:
if p1 - p2 in s and p1 != p2 and p1 == s[p1 - p2][1]:
import primes
# find a*b for which n^2 + an + b generates the most consecutive primes
# b is a prime
primesB = primes.populatePrimes(1000)
primes = set(primes.populatePrimes(10000))
aList = [n for n in range(-999, 1000) if n % 2 != 0]
answers = {} #key = number of consec primes generated, val = a*b
for a in aList:
for b in primesB:
quad = lambda x: x**2 + a * x + b
composite = False
num = 0
while not composite:
if quad(num) not in primes:
composite = True
else:
num += 1
#answers[a*b] = num
answers[num] = (a, b)
print max(answers)
print answers[max(answers)]
import primes p = primes.populatePrimes(1000)[3:] max = (0, 0) for prime in p: count = 1 divis = False while not divis: #print "We are on prime %d and count %d" %(prime, count) if ((10**count - 1) % prime) == 0: divis = True else: count += 1 if count > max[1]: max = (prime, count) print max