class Problem58: def __init__(self): self.primeChecker = PrimeChecker() self.primeChecker.initPrimeFactoring() def getDiagonalsFromSpiralOfSize(self, size, diagonals=None): counter = 1 if diagonals == None: diagonals = [] for i in range(0, int((size-1)/2)): for _ in range(0, 4): counter += 2 + 2*i diagonals.append(counter) else: i = int((size-1)/2) - 1 counter = int(diagonals[-1]) for _ in range(0, 4): counter += 2 + 2*i diagonals.append(counter) return diagonals def answer(self): size = 1 ratio = 100 diagonals = None totalPrimes = 0 while ratio >= 0.10: size += 2 diagonals = self.getDiagonalsFromSpiralOfSize(size, diagonals) total = (size-1)/2 * 4 + 1 totalPrimes += len([x for x in diagonals[-4:-1] if self.primeChecker.isPrime(x)]) ratio = totalPrimes / total return size
def hasPrimeVariations(self, number, replaceDigit, primeVariations): primeCount = 0 for i in range(0, 10): testNumber = number.replace(replaceDigit, str(i)) if PrimeChecker.isPrime(int(testNumber)) \ and self.hasEqualNumberOfDigits(testNumber, number): primeCount += 1 return primeCount == primeVariations
def triSequenceIsPrimeAndPermutation(self, start, step): for n in range(0, 3): if not PrimeChecker.isPrime(start+n*step): return False for n in range(0, 2): if not self.isPermutationOf(n, start): return False return True
def getLongestSumOfConsecutivePrimesBelow(self, n): longestSequenceLength = 0 longestSum = 0 primes = PrimeChecker.primesBelow(n) for i in range(0, len(primes)): for j in range(i+1, len(primes)-1): primeSum = sum(primes[i:j]) if primeSum >= n: break if PrimeChecker.isPrime(primeSum) and j - i > longestSequenceLength: longestSequenceLength = j - i longestSum = primeSum return longestSequenceLength, longestSum
class Problem60: def __init__(self, primeLimit): self.primeChecker = PrimeChecker() self.primeChecker.initPrimeFactoring() self.primes = PrimeChecker.primesBelow(primeLimit) self.primes.remove(2) self.pairs = self.buildPairs(self.primes) def buildPairs(self, primes): pairs = dict() for p1 in primes: if p1 == 5: continue pairs[p1] = set() for q in range(primes.index(p1), len(primes)): p2 = primes[q] if self.primeChecker.isPrime(int(str(p1) + str(p2))) and \ self.primeChecker.isPrime(int(str(p2) + str(p1))): pairs[p1].add(p2) return pairs def answer(self): lowest = 10000000 for p1 in self.pairs: for p2 in self.pairs[p1]: setA = self.pairs[p1] & self.pairs[p2] if len(setA) > 0: for p3 in setA: setB = setA & self.pairs[p3] if len(setB) > 0: for p4 in setB: setC = setB & self.pairs[p4] if len(setC) > 0: total = sum([p1, p2, p3, p4] + list(setC)) if total < lowest: lowest = total return lowest
def test_27ShouldNotBeAPrime(self): self.assertFalse(PrimeChecker.isPrime(27))
def test_47ShouldBeAPrime(self): self.assertTrue(PrimeChecker.isPrime(47))