def PE87(L):
P = set()
p = prime_sieve(int(sqrt(L)))
for a in p:
for b in p:
qz = a**4 + b**3
if qz >= L: break
for c in p:
z = c**2 + qz
if z >= L: break
P.add(z)
return len(P)
def PE87(L):
P = set()
p = prime_sieve(int(sqrt(L)))
for a in p:
for b in p:
qz = a**4 + b**3
if qz >= L: break
for c in p:
z = c**2 + qz
if z >= L: break
P.add(z)
return len(P)
#Project Euler Problem 133 #http://blog.dreamshire.com/project-euler-133-solution/ from projecteuler import prime_sieve L, q, s = 100000, pow(10, 20), 2+3 s += sum(p for p in prime_sieve(L)[2:] if pow(10, q, p) != 1) print "Project Euler 133 Solution = ", s
#http://blog.dreamshire.com/project-euler-231-solution/
#Project Euler Problem 231
from projecteuler import prime_sieve
n, r, s = 20000000, 15000000, 0
for p in prime_sieve(n):
pj = p
while pj <= n:
s += p * (n//pj - r//pj - (n - r)//pj)
pj *= p
print "Project Euler 231 Solution =", s
#http://blog.dreamshire.com/project-euler-249-solution/
#Project Euler Problem 249
from projecteuler import prime_sieve, is_prime
primes = prime_sieve(5000)
t = [1] + [0] * sum(primes)
sp = 0
for p in primes:
sp += p
for j in range(sp, p - 1, -1):
t[j] = (t[j] + t[j - p])
print "Project Euler 249 Solution =", (sum(t[p]
for p in range(sp) if is_prime(p)) %
10**16)
#http://blog.dreamshire.com/project-euler-249-solution/
#Project Euler Problem 249
from projecteuler import prime_sieve, is_prime
primes = prime_sieve(5000)
t = [1] + [0] * sum(primes)
sp = 0
for p in primes:
sp += p
for j in range(sp, p-1, -1):
t[j] = (t[j] + t[j-p])
print "Project Euler 249 Solution =", (sum(t[p] for p in range(sp) if is_prime(p)) % 10**16)
#http://blog.dreamshire.com/project-euler-231-solution/
#Project Euler Problem 231
from projecteuler import prime_sieve
n, r, s = 20000000, 15000000, 0
for p in prime_sieve(n):
pj = p
while pj <= n:
s += p * (n // pj - r // pj - (n - r) // pj)
pj *= p
print "Project Euler 231 Solution =", s
#Project Euler Problem 133 #http://blog.dreamshire.com/project-euler-133-solution/ from projecteuler import prime_sieve L, q, s = 100000, pow(10, 20), 2 + 3 s += sum(p for p in prime_sieve(L)[2:] if pow(10, q, p) != 1) print "Project Euler 133 Solution = ", s
