def p231():
u = Utils()
primes = u.sieve(20000000)
total = 0
for p in primes:
total += p * (f.v(20000000, p) - (f.v(5000000, p) + f.v(15000000, p)))
return total
def p46():
#getting precalculated primes and squares:
u = Utils()
primes = u.sieve(6000)
squares = [i * i for i in range(1, 101)]
#start searching at 15:
o = 15
while o < 5800:
#is the test number prime?
if u.chop(o, primes) != -1:
#yeap, go to next one:
o += 2
continue
#nope, begin testing:
ind = 0
found = False
while o - primes[ind] > 0:
s = (o - primes[ind]) / 2
#found desired decomposition?
if u.chop(s, squares) != -1:
#yep, break out:
found = True
break
#nope, try next prime:
else:
ind += 1
#found possible candidate:
if not found:
return o
#keep searching:
o += 2
def p35():
u = Utils()
sieve = u.sieve(10**6)
count = 0
for prime in sieve:
s = str(prime)
l = cyclic_shifts_of(s)
if all_in(l, sieve, u):
count += 1
return count
def p44():
u = Utils()
limit = 3000
pl = [f.p(i) for i in range(limit)]
for a in range(1, limit):
for b in range(1, limit):
if a > b:
c = pl[a] + pl[b]
d = pl[a] - pl[b]
if u.chop(c, pl) > -1 and u.chop(d, pl) > -1:
print(a, b, pl[a], pl[b], pl[pl.index(c)], pl.index(c),
pl[pl.index(d)], pl.index(d))
def test_is_prime_corner_cases():
u = Utils()
actual_prime = u.is_prime(2)
assert(actual_prime == True)
actual_prime = u.is_prime(3)
assert(actual_prime == True)
actual_prime = u.is_prime(4)
assert(actual_prime == False)
actual_prime = u.is_prime(5)
assert(actual_prime == True)
# A composite is a number containing at least two prime
# factors. For example, 15 = 3 × 5; 9 = 3 × 3; 12 = 2 × 2
# × 3.
#
# There are ten composites below thirty containing precisely
# two, not necessarily distinct, prime factors: 4, 6, 9, 10,
# 14, 15, 21, 22, 25, 26.
#
# How many composite integers, n < 10^8, have precisely two,
# not necessarily distinct, prime factors?
from euler.utils import Utils
from math import sqrt
from bisect import bisect
u = Utils()
#One of the accepted solutions from the forum (by
#logopetria, @Sat, 22 Mar 2008, 08:45):
primes = u.sieve(5 * (10**7))
def p187():
N = 10**8
total = 0
for x in range(bisect(primes, sqrt(N))):
p = primes[x]
total += bisect(primes, N / p) - x
return total
def test_to_matrix_2():
u = Utils()
u.to_matrix('./test_matrix_2.in', separator=',')
def test_is_composite():
u = Utils()
actual_prime = u.is_prime(2200)
assert(actual_prime == False)
def test_sieve_set():
u = Utils()
primes = u.sieve_set(50)
assert(primes == set([2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]))
def test_is_prime():
u = Utils()
actual_prime = u.is_prime(31)
assert(actual_prime == True)
def test_to_matrix():
u = Utils()
u.to_matrix('./test_matrix.in')
def test_log_nPr():
u = Utils()
actual = u.log_nPr(5, 4)
assert(actual > 0)
def test_log_factorial():
u = Utils()
actual = u.log_factorial(5)
assert(actual > 0)
def all_in(l1, l2, u):
u = Utils()
for n in l1:
if u.chop(n, l2) == -1:
return False
return True