def challenge058():
current = 1
total = 1
nPrimes = 0
diagonals = 1
primeChecker = PrimeChecker()
# Cycle through layers
sidestep = 2
while True:
for j in xrange(1, 4):
current += sidestep
if primeChecker.isPrime(current):
nPrimes += 1
current += sidestep
diagonals += 4
if nPrimes * 10 < diagonals:
return sidestep + 1
sidestep += 2
def challenge077():
pc = PrimeChecker()
nums = dict()
num = 2
while True:
sums = set()
# Is the current number a prime?
if pc.isPrime(num):
sums.add(tuple([num]))
# Check for previous sums
for a in xrange(2, num // 2 + 1):
b = num - a
# Collect each a sum to each b sum
for abSums in [sorted(aSum + bSum) for aSum in nums[a] for bSum in nums[b]]:
sums.add(tuple(abSums))
nums[num] = sums
if len(sums) > 5000:
return num
num += 1
def challenge051():
pc = PrimeChecker()
step = cycle([2, 4])
current = 5
while True:
# Check current
if pc.isPrime(current) and has3SameDigits(current):
# Substitute 0 to 9
w = str(current)
for i in xrange(0, 10):
nPrimes, smallest = substitutePrimes(w, str(i), pc)
if nPrimes == 8:
return smallest
current += step.next()
