def main():
start = time()
primeSet = set([])
solutionSet = set([])
for i in xrange(2, LIMIT + 1):
if isPrime(i):
primeSet.add(str(i))
for prime in primeSet:
tempPrime = prime
isSolution = True
for iteration in xrange(len(prime) - 1):
tempPrime = tempPrime[1:] + tempPrime[0]
if tempPrime not in primeSet:
isSolution = False
break
if isSolution:
solutionSet.add(prime)
print "Solution set size: ", len(solutionSet)
end = time()
print "Runtime: ", end - start, " seconds."
def main():
start = time()
primeSet = set([])
solutionSet = set([])
for i in xrange(2, LIMIT + 1):
if isPrime(i):
primeSet.add(str(i))
for prime in primeSet:
tempPrime = prime
isSolution = True
for iteration in xrange(len(prime) - 1):
tempPrime = tempPrime[1:] + tempPrime[0]
if tempPrime not in primeSet:
isSolution = False
break
if isSolution:
solutionSet.add(prime)
print "Solution set size: ", len(solutionSet)
end = time()
print "Runtime: ", end - start, " seconds."
def main():
start = time()
primeSet = set([])
solutionSet = set([])
candidate = str(11) # skip 2,3,5,7 as per the question.
while len(solutionSet) != SOLUTION_LIMIT:
if checkCandidateWorthiness(candidate):
isPrimeFromLeftTruncation = True
for number in produceNumbersFromLeftTruncation(candidate):
if number not in primeSet:
if isPrime(number):
primeSet.add(number)
else:
isPrimeFromLeftTruncation = False
break
isPrimeFromRightTruncation = True
if isPrimeFromLeftTruncation:
for number in produceNumbersFromRightTruncation(candidate):
if number not in primeSet:
if isPrime(number):
primeSet.add(number)
else:
isPrimeFromRightTruncation = False
break
if isPrimeFromLeftTruncation and isPrimeFromRightTruncation:
solutionSet.add(int(candidate))
candidate = str(int(candidate) + 1)
end = time()
print "Solutions: ", solutionSet
print "Sum: ", sum(solutionSet)
print "Runtime: ", end - start, " seconds."
def main():
start = time()
primeSet = set([])
solutionSet = set([])
candidate = str(11) # skip 2,3,5,7 as per the question.
while len(solutionSet) != SOLUTION_LIMIT:
if checkCandidateWorthiness(candidate):
isPrimeFromLeftTruncation = True
for number in produceNumbersFromLeftTruncation(candidate):
if number not in primeSet:
if isPrime(number):
primeSet.add(number)
else:
isPrimeFromLeftTruncation = False
break
isPrimeFromRightTruncation = True
if isPrimeFromLeftTruncation:
for number in produceNumbersFromRightTruncation(candidate):
if number not in primeSet:
if isPrime(number):
primeSet.add(number)
else:
isPrimeFromRightTruncation = False
break
if isPrimeFromLeftTruncation and isPrimeFromRightTruncation:
solutionSet.add(int(candidate))
candidate = str(int(candidate) + 1)
end = time()
print "Solutions: ", solutionSet
print "Sum: ", sum(solutionSet)
print "Runtime: ", end - start, " seconds."
def checkCandidateWorthiness(number):
if '0' in number:
return False
if number[-1] not in SINGLE_DIGIT_PRIME_SET:
return False
if number[0] not in SINGLE_DIGIT_PRIME_SET:
return False
if number[:2] not in DOUBLE_DIGIT_PRIME_SET:
return False
if not isPrime(number):
return False
return True
def checkCandidateWorthiness(number):
if '0' in number:
return False
if number[-1] not in SINGLE_DIGIT_PRIME_SET:
return False
if number[0] not in SINGLE_DIGIT_PRIME_SET:
return False
if number[:2] not in DOUBLE_DIGIT_PRIME_SET:
return False
if not isPrime(number):
return False
return True
def main():
start = time()
primeSet = set([])
squaredDict = {}
candidate = 11 # 3, 5, 7 are prime. 9 is given to not break the conjecture
solution = 0
while solution == 0:
if candidate not in primeSet and not isPrime(candidate):
createdUsingPrime = False
for i in xrange(1, int(ceil(
sqrt(candidate /
2)))): # only check natural numbers for primality
if i not in squaredDict:
squaredDict[i] = 2 * i**2
remainderValue = candidate - squaredDict[i]
if remainderValue in primeSet or isPrime(remainderValue):
primeSet.add(remainderValue)
createdUsingPrime = True
break
if not createdUsingPrime:
solution = candidate
else:
primeSet.add(candidate)
candidate += 2
print "Smallest odd, composite number that breaks the conjecture: ", solution
end = time()
print "Runtime: ", end - start, " seconds."
def main():
start = time()
primeSet = set([])
squaredDict = {}
candidate = 11 # 3, 5, 7 are prime. 9 is given to not break the conjecture
solution = 0
while solution == 0:
if candidate not in primeSet and not isPrime(candidate):
createdUsingPrime = False
for i in xrange(1, int(ceil(sqrt(candidate / 2)))): # only check natural numbers for primality
if i not in squaredDict:
squaredDict[i] = 2 * i ** 2
remainderValue = candidate - squaredDict[i]
if remainderValue in primeSet or isPrime(remainderValue):
primeSet.add(remainderValue)
createdUsingPrime = True
break
if not createdUsingPrime:
solution = candidate
else:
primeSet.add(candidate)
candidate += 2
print "Smallest odd, composite number that breaks the conjecture: ", solution
end = time()
print "Runtime: ", end - start, " seconds."
def run():
primes = set([x for x in range(1000, 9999+1) if isPrime(x)])
primesByPerm = {}
groups = []
for x in primes:
primesByPerm[x] = identity(x)
for v in primesByPerm.values():
blah = sorted([x for x in primesByPerm.keys() \
if primesByPerm[x] == v])
if blah not in groups:
groups.append(blah)
for x in groups:
if len(x) >= 3:
#print(x)
constDiffCheck(x)
'''
Created on Jun 12, 2009
@author: anon
'''
import math
from ProjectEulerLibrary import getPrimes, isPrime
n = 1000000
primes = getPrimes(math.ceil(n/2))
maxLength = 0
maxLengthSum = 0
for i in range(len(primes)):
sum = 0
length = 0
for y in primes[i:]:
sum += y
if sum >= n:
break
if isPrime(sum) and length > maxLength:
maxLengthSum = sum
maxLength = length
length += 1
print(maxLengthSum)
'''
Created on Apr 12, 2009
@author: anon
'''
from ProjectEulerLibrary import isPrime, isPandigital
for n in range(1,9000000):
if isPandigital(n) and isPrime(n):
print(n)
'''
Created on Apr 17, 2009
@author: anon
'''
from ProjectEulerLibrary import isPrime
truncatablePrimes = []
for n in range(10,740000+1):
if isPrime(n):
prime = True
for x in range(len(str(n))):
left = [int(y) for y in str(n)]
right = [int(y) for y in str(n)]
for y in range(x+1):
left.pop(0)
right.pop(-1)
if len(left) == 0 or len(right) == 0:
break
if len(left) == 1:
left = left[0]
else:
left = int(''.join([str(y) for y in left]))
if len(right) == 1:
right = right[0]
else:
from ProjectEulerLibrary import isPrime
# find odd non-prime that != prime + 2*square
# iterate on odd non-prime numbers starting with... 9
# 2*2 + 5
done = False
compositeOdd = (x for x in range(3,10000000000) if x%2 == 1 and not isPrime(x))
while not done:
canBeWritten = False
x = next(compositeOdd)
i = 1
amt = 2*(i**2)
while amt <= x:
print('x: ', x)
print('amt: ', amt)
if isPrime(x - amt):
canBeWritten = True
break
i += 1
amt = 2*(i**2)
if not canBeWritten:
print(x)
done = True
'''
Created on Apr 12, 2009
@author: anon
'''
from ProjectEulerLibrary import isPrime
maxPrimeCount = 0
coeffProd = 1
lastWasPrime = True
for b in [x for x in range(1,1000) if isPrime(x)]:
for a in range(-999, 999):
primeCount = 0
n = 0
while isPrime(n**2 + a*n + b):
primeCount = primeCount + 1
n = n + 1
if primeCount > maxPrimeCount:
maxPrimeCount= primeCount
coeffProd = a * b
print('a=%s b=%s' % (a,b))
print(coeffProd)
'''
Created on Apr 18, 2009
@author: anon
'''
from ProjectEulerLibrary import isPrime
primeCount = 0
compositeCount = 0
n = 1
skipAmount = 1
while skipAmount <= 100000:
for i in range(4):
n = n + (skipAmount + 1)
if isPrime(n):
primeCount = primeCount + 1
else:
compositeCount = compositeCount + 1
ratio = primeCount / (compositeCount + primeCount)
if ratio * 100 < 10:
print(skipAmount)
break
skipAmount = skipAmount + 2