def below(M):
m = int(sqrt(M - (2**3 + 2**4)))
print "need primes less than %s" % m
primes = list(prime_gen(max_size = m))
nums = set([])
for p1 in primes:
if p1**2 + 2**3 + 2**4 > M:
break
for p2 in primes:
if p1**2 + p2**3 + 2**4 > M:
break
for p3 in primes:
if p1**2 + p2**3 + p3**4 > M:
break
nums.add(p1**2+p2**3+p3**4)
return len(nums)
from math import sqrt
from helpers import cached_prime, prime_gen, factor
def totient(n, f):
prod = 1
for p in f:
prod *= (1 - float(1) / p)
return int(round(prod * n))
def is_perm(n1, n2):
return sorted(str(n1)) == sorted(str(n2))
limit = 10**7
primes = list(prime_gen(max_size = limit/2 ))
m = limit
for p in reversed(primes):
for p2 in primes:
if p*p2 > limit:
break
t = totient(p*p2, (p, p2))
if is_perm(p*p2, t):
if m > float(p)*p2/t:
m = float(p)*p2/t
print(p*p2, t, float(p)*p2/t)
from helpers import factor, cached_prime, prime_gen
from math import sqrt
def totient(n):
f = factor(n)
prod = 1
for p in f:
prod *= (1 - float(1) / p)
return int(round(prod * n))
limit = 1000000
cached_prime(1000000)
prod = 1
for p in prime_gen():
prod *= p
if prod <= limit:
t = totient(prod)
print (prod, t, float(prod) / t)
else:
break
return (left, right)
def is_family(f):
for i in range(len(f)):
for j in range(i + 1, len(f)):
left = int_concat(f[i], f[j])
right = int_concat(f[j], f[i])
if not (is_prime(left) and is_prime(right)):
return False
return True
sieve(100000000)
max_prime = 10000
fam_size = 3
primes = list(prime_gen(max_size = max_prime))
def fams():
for i in range(1, len(primes)):
for j in range(i+1, len(primes)):
if not is_family((primes[i], primes[j])):
continue
print (primes[i], primes[j])
for k in range(j+1, len(primes)):
if not is_family((primes[i], primes[j], primes[k])):
continue
for l in range(k + 1, len(primes)):
if not is_family((primes[i], primes[j], primes[k], primes[l])) or k > l:
continue
for m in range(l + 1, len(primes)):
if not is_family((primes[i], primes[j], primes[k], primes[l], primes[m])):
continue