def isCircular(n):
s = str(n)
ns = map(lambda x: int(rotate(s, x)), range(1, len(s) + 1))
for n in ns:
if not isPrime(n):
return False
return True
def calc():
corner = 1
size = 2
nonPrime = [1]
prime = []
i = 3
while True:
# loop through this layer
for _ in range(4):
corner += size
if isPrime(corner):
prime.append(corner)
else:
nonPrime.append(corner)
# calculate new ratio
corners = len(nonPrime) + len(prime)
primes = len(prime)
ratio = primes / corners
print("i=", i, corners, primes, ratio)
if ratio < 0.10:
break
size += 2
i += 2
return i
def problem357(n):
divs = divisors(n)
for d in divs:
a = d + n // d
if not isPrime(a):
return False
return True
def canConcat(ps):
for a, b in permutations(ps, 2):
if not isPrime(int(str(a) + str(b))):
return False
#else:
# print(a, b, str(a) + str(b))
return True
def problem51():
i = 0
while True:
i += 1
if i % int(1e5) == 0:
print(i)
if not isPrime(i):
continue
ans = test(i)
if ans != False:
print(ans)
break
def problem49():
for n in range(1000, 10000):
if not isPrime(n):
continue
for a in range(1000, 10000):
ns = [n]
total = n
while len(ns) != 3:
total = total + a
if total > 9999:
break
nextN = total
if isPrime(nextN) and isPerm(n, nextN):
ns.append(nextN)
else:
break
if len(ns) == 3:
print(ns)
# [1487, 4817, 8147]
# [2969, 6299, 9629]
# 0:00:16.765959 ELAPSED
def problem131():
b = 1**3
a = 2**3
diff = a - b
i = 3
count = 0
while diff < int(1e6):
if isPrime(diff):
count += 1
b = a
a = i**3
i += 1
diff = a - b
print(count)
return
i = 2
count = 0
ratio = 0
while True:
cube = i * i * i
i += 1
#print(i)
if ratio != 0:
lowerBound = int(ratio * i)
else:
lowerBound = 1
for n in range(lowerBound, i - 1):
n3 = n * n * n
n2 = n * n
p = (cube - n3) // n2
eq = n3 + n2 * p
if eq == cube:
if p in primes:
count += 1
ratio = n / i
print("i =", i, "n =", n, "p =", p, eq, "=", cube, count,
"below", i)
#print(cube - n3 == p * n2)
print("p + n", p + n, (p + n**(1.0 / 3.0)), "\n")
#print(p, eq, eq == cube)
if i >= limit:
break
print(count, "below", limit)
def problem387():
primes = filter(isPrime, range(1, int(1e5)))
bases = set()
total = 0
for p in primes:
n = chop(p)
if strongTrunc(n):
print(p, str(p)[:2])
bases.add(str(p)[:2])
total += p
#print(total)
s = list(bases)
s.sort()
print(s, len(s))
print(
sum(
filter(lambda x: strongTrunc(chop(x)) and isPrime(x),
range(1, int(1e4)))))
def isStrong(n):
return isPrime(n / sum(map(int, str(n))))
def p(n):
print(primeFactors(n))
print(isPrime(n))