def consecutivePrimes(a, b):
n = 0
while (True):
quadradicResult = quadratic(n, a, b)
if isPrime(quadradicResult) == False:
return n
n += 1
def getFactors(input):
factors = []
for i in range(1, int(sqrt(input)+1)):
if input % i == 0:
factors.append(i)
factors.append(int(input/i))
return list(filter(lambda x: x != 1 and isPrime(x), factors))
def getRelativePrimes(n):
if isPrime(n):
rps = list(range(n))
rps.pop(0)
return rps
factorsOfN = getFactorsWithout1(n)
factorsMap[n] = factorsOfN
rp = []
for i in range(1, n):
factorsOfI = getFactorsWithout1(i)
if not hasCommon(factorsOfI, factorsOfN):
rp.append(i)
return rp
def getFamily(replacedDigits, baseNumber, maxNonPrimes):
bnAsStr = list(str(baseNumber))
nonPrimeCount = 0
family = []
if bnAsStr[replacedDigits[0]] != bnAsStr[replacedDigits[1]]:
return family
for i in range(0, 10):
for dig in replacedDigits:
bnAsStr[dig] = str(i)
if not isPrime(int(''.join(bnAsStr))):
nonPrimeCount += 1
if nonPrimeCount > maxNonPrimes:
return []
else:
family.append(int(''.join(bnAsStr)))
return family
print('project euler problem 3')
from utils.mathHelpers import isPrime
from math import sqrt
lim = 600851475143
sqlimit = sqrt(lim)
factors = []
for i in range(1, int(sqlimit)):
if lim % i == 0 and isPrime(i):
factors.append(i)
print(factors)
if (srcs.count(ch) != tgts.count(ch)):
return False
return True
print('isPerm', isPerm(123, 312))
print('isPerm2', isPerm(1487, 4817))
print('isPerm3', isPerm(4817, 8147))
print('isPerm4', isPerm(213, 512))
print ('isPerm5', isPerm(6733, 6673))
for starting in range(100, 10000):
if (not isPrime(starting)):
continue
for incr in range(0, 3335):
for i in range(1, 3):
curr = starting + (i * incr)
if (not isPrime(curr)):
break
if (not isPerm(curr, starting)):
break
if (i == 2):
print('curr is ', curr)
print('starting is ', starting)
print('incr is ', incr)
family = []
if bnAsStr[replacedDigits[0]] != bnAsStr[replacedDigits[1]]:
return family
for i in range(0, 10):
for dig in replacedDigits:
bnAsStr[dig] = str(i)
if not isPrime(int(''.join(bnAsStr))):
nonPrimeCount += 1
if nonPrimeCount > maxNonPrimes:
return []
else:
family.append(int(''.join(bnAsStr)))
return family
print("isPrime", not isPrime(86507))
# brute force:
# step thru each permutation of swapped indexes, index 1, index 2... index 1 and 2, index 1 and 3 ...
# fix some digits swap some digits. then for each
# fixed number and idx pair, try 0-9 (10 ops), for each item that matches, add 1 to the count
# permutations of abcde - ab ac ad ae
def getPossibleReplacements(max):
replacementIndexes = []
for i in range(0, max):
for j in range(i, max):
for k in range(j, max):
newList = [i, j, k]
replacementIndexes.append(newList)
return replacementIndexes
print('project euler problem 41')
from utils.mathHelpers import isPandigital, isPrime
from euler32 import getAllPerms, stringifyAndJoin
allPerms = [stringifyAndJoin(i) for i in getAllPerms([1, 2, 3, 4, 5, 6, 7])]
for cand in range(0, len(allPerms)):
print('is prime', isPrime(allPerms[cand]))
filtered = [j for j in allPerms if isPrime(j) == True]
print('filtered is ', filtered)
print('project euler problem 27')
from utils.mathHelpers import isPrime
print('isPrime(7) is {}'.format(isPrime(7)))
print('isPrime(8) is {}'.format(isPrime(8)))
print('isPrime(10) is {}'.format(isPrime(10)))
print('isPrime(11) is {}'.format(isPrime(11)))
def quadratic(n, a, b):
return n**2 + n * a + b
def consecutivePrimes(a, b):
n = 0
while (True):
quadradicResult = quadratic(n, a, b)
if isPrime(quadradicResult) == False:
return n
n += 1
longestStreak = 0
longesta = -1000
longestb = -1000
for a in range(-1000, 1001):
for b in range(-1000, 1001):
cur = consecutivePrimes(a, b)
if (cur > longestStreak):
longestStreak = cur
print('project euler problem 37')
import math
from utils.mathHelpers import isPrime
def getIterations(asStr):
iterations = set()
for idx in range(0, len(asStr)):
# compare first and last
subStr = asStr[idx:len(asStr)]
subStr2 = asStr[0:idx+1]
iterations.add(int(subStr))
iterations.add(int(subStr2))
return iterations
passed = []
for idx in range(10, 1000000):
iter = getIterations(str(idx))
passes = True
for item in iter:
if (not(isPrime(item))):
passes = False
break
if (passes):
passed.append(idx)
print('passed is ', passed)
print('sum is ', sum(passed))
from utils.mathHelpers import isPrime
print('project euler problem 50')
primesToOneM = []
for i in range(1, 1000001):
if (isPrime(i)):
primesToOneM.append(i)
print(primesToOneM)
print('len is ', len(primesToOneM))
print(sum(primesToOneM[3:546]))
longestSplit = 0
lower = 0
upper = 0
for i in range(0, 1000):
print('i is now ', i)
for j in range(1, 1000):
if (j - i < longestSplit):
continue
curSum = sum(primesToOneM[i:j])
print('curSum is ', curSum)
if curSum in primesToOneM:
split = j - i
if (split > longestSplit):
lower = i
upper = j
longestSplit = split
def getRatioOfPrimesOnDiagonal(diagonals):
primeDiags = list(filter(lambda x: isPrime(x), list(diagonals)))
return len(primeDiags) / len(list(diagonals))
from math import sqrt
from utils.mathHelpers import isPrime
print('project euler problem 46')
print(isPrime(33))
composites = []
primes = []
doubleOfSquares = []
for i in range(4, 4000):
nextOdd = (2 * i) + 1
if (not isPrime(nextOdd)):
composites.append(nextOdd)
for i in range(0, 4000):
nextOdd = (2 * i) + 1
if (isPrime(nextOdd)):
primes.append(nextOdd)
for i in range(0, 100):
nextItem = 2 * (i**2)
doubleOfSquares.append(nextItem)
print("composites is ", composites)
print("primes is ", primes)
print("double of squares", doubleOfSquares)
def isBuildable(input):
result = False
for i in range(0, len(primes)):
newString = ''
for idx in range(0, len(asStr) - 1):
newString += asStr[idx + 1]
newString += asStr[0]
return newString
def getRotations(input):
asStr = str(input)
rotations = []
rotations.append(int(asStr))
for _ in range(0, len(asStr) - 1):
asStr = getNextRotation(asStr)
rotations.append(int(asStr))
return rotations
primes = []
for cur in range(0, 1000000):
rots = getRotations(cur)
prime = True
for i in range(0, len(rots)):
if isPrime(rots[i]) != True:
prime = False
if (prime):
primes.append(cur)
print("prime for {} is {}".format(cur, prime))
print("primes is ", len(primes))
