def pe41():
"""
>>> pe41()
7652413
"""
primes = Primes(1000000)
for perm in permutations(range(7, 0, -1)):
n = list_num(perm)
if primes.is_prime(n):
return n
return -1
def pe49(limit=10000):
"""
>>> pe49()
(2969, 6299, 9629)
"""
pr = Primes()
for num in range(1111, limit):
sn = str(num)
if sn.find('0') >= 0: continue
if pr.is_prime(num):
pp = {num : 1}
for p in permutations(list(sn)):
n = int(''.join(p))
if pr.is_prime(n):
pp[n] = 1
primes = sorted(pp.keys())
pl = len(primes)
for a in range(pl):
if primes[a] == 1487: continue
for b in range(a+1, pl):
c = (primes[a] + primes[b]) >> 1
if c in pp:
return (primes[a], c, primes[b])
return None
def pe27():
"""
>>> pe27()
(-59231, (-61, 971, 71))
"""
m = (0, 0, 0)
primes = Primes(15000)
for a in range(-999, 1000):
for b in range(max(2, 1 - a), 1000):
n, cnt = 0, 0
while 1:
p = n * (n + a) + b
if primes.is_prime(p):
cnt += 1
else:
break
n += 1
if cnt > m[2]:
m = (a, b, cnt)
return (m[0] * m[1], m)
def pe27():
"""
>>> pe27()
(-59231, (-61, 971, 71))
"""
m = (0, 0, 0)
primes = Primes(15000)
for a in range(-999, 1000):
for b in range(max(2, 1 - a), 1000):
n, cnt = 0, 0
while 1:
p = n * (n + a) + b
if primes.is_prime(p):
cnt += 1
else:
break
n += 1
if cnt > m[2]:
m = (a, b, cnt)
return (m[0] * m[1], m)
from primes import Primes
n = i = 1
p = Primes()
percent = 1
diagonals = 1 # this takes into account the center (1)
prime_diagonals = 0
while percent > 0.1:
for x in range(4):
n+=2*i
prime_diagonals += p.is_prime(n)
diagonals += 4
i+=1
percent = float(prime_diagonals) / diagonals
print prime_diagonals, '/', diagonals, ',', percent
print 'side =', int(n**(0.5)), 'primes =', prime_diagonals, '/', diagonals, percent
"""
project euler #77
matt donahoe
i enjoyed thinking of this one. did some back of the envelope (literally)
discovered a dynamic programming solution
"""
from primes import Primes
p=Primes(5000)
ways = {} #ways.get((n,p),0) = number of ways to sum to n using only primes >= p
primes = []
n=1
while s<=50000000:
n+=1
s = 0
if p.is_prime(n):
s = 1
primes.append(n)
for x in primes[::-1]:
s+=ways.get((n-x,x),0)
ways[(n,x)] = s
print n,s
# For the moment the maximum sequence has 0 length
# Each time we find a longer sequence we will record it here
# together with its parameters (point in the square, ...)
maxi = {'n': 0}
for a, b in get_coeffs(N):
i = a + N - 1 # indices in the matrix
j = b + N - 1
f = make_fun(a, b)
# how many primes does f produces?
n = 0
while True:
p = f(n)
if not primes.is_prime(p):
break
else:
pass
n += 1
# records number of primes in the matrix
matrix[i][j] = n
# if we have found a better sequence, we save it in 'maxi'
if n > maxi['n']:
maxi = {'n': n, 'f': f}
print(f.format(), " ------> ", maxi['n'])
# print ("===============================================================", a, b, n)
# For the moment the maximum sequence has 0 length
# Each time we find a longer sequence we will record it here
# together with its parameters (point in the square, ...)
maxi = {'n': 0}
for a, b in get_coeffs(N):
i = a + N - 1 # indices in the matrix
j = b + N - 1
f = make_fun(a, b)
# how many primes does f produces?
n = 0
while True:
p = f(n)
if not primes.is_prime(p):
break
else:
pass
n += 1
# records number of primes in the matrix
matrix[i][j] = n
# if we have found a better sequence, we save it in 'maxi'
if n > maxi['n']:
maxi = {'n': n, 'f': f}
print (f.format(), " ------> ", maxi['n'])
# print ("===============================================================", a, b, n)
