def is_prime_permute(n):
perms = [int(''.join(x)) for x in list(it.permutations(str(n), 4))]
perms = list(set(perms))
perms_prime = [x for x in perms if fns.is_prime(x)]
perms_diff = [[abs(x - y) for x in perms_prime] for y in perms_prime]
perms_diff_count = [is_multi_count(x) for x in perms_diff]
return any(perms_diff_count)
def nth_prime(n):
prime_counter = 2
num_counter = 5
while 1 > 0:
if fns.is_prime(num_counter):
prime_counter += 1
if prime_counter == n:
return num_counter
num_counter += 2
# 8. n consecutive numbers with higest product
n = 13
long_number = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
products = []
for i in xrange(n - 1, len(long_number)):
products.append(reduce(lambda x, y: int(x) * int(y), long_number[(i - n + 1):(i + 1)]))
print "Euler 8:", max(products),
print "T:", time() - start; start = time()
# 9. Pythagoeran triplet summing to 1000
n = 1000
for a in xrange(2, int(n/3)):
for b in xrange(2, n):
c = n - a - b
if (a*a + b*b == c*c):
output = a, b, c
break
print "Euler 9:", output[0] * output[1] * output[2],
print "T:", time() - start; start = time()
# 10. Sum of all primes below n
n = int(2e6)
prime_sum = 2
for i in xrange(3, n, 2):
if fns.is_prime(i):
prime_sum += i
print "Euler 10:", prime_sum,
print "T:", time() - start; start = time()
if int(i[6:9]) % 13 != 0: continue
if int(i[7:10]) % 17 != 0:continue
all_nums.append(int(i))
print "Euler 43:", sum(all_nums),
print "T:", time.time() - start; start = time.time()
# Triangle numbers
def word_val_sum(word): return sum([ord(x) - ord("A") + 1 for x in word])
def gen_triangle_numbers(n): return [i * (i + 1) / 2 for i in xrange(1,n)]
word_list = str.replace(open("../Data/Interesting/euler/42.txt", 'r').read(), '"', '').split(',')
word_values = map(word_val_sum, word_list)
triangle_numbers = gen_triangle_numbers(50)
triangles_in_list = [x for x in word_values if x in triangle_numbers]
print "Euler 42:", len(triangles_in_list),
print "T:", time.time() - start; start = time.time()
# Largest Pandigital prime
for i in xrange(7654321, 0, -1):
if "".join(sorted(str(i))) == "1234567":
if(fns.is_prime(i)):
break
print "Euler 41:", i,
print "T:", time.time() - start; start = time.time()
if len(mult_sum) >= 9:
if "".join(sorted(mult_sum)) == '123456789':
all_pans.append(int(mult_sum))
break
j += 1
print "Euler 38:", max(all_pans),
print "T:", time.time() - start; start = time.time()
# Truncatable primes
perms = ['1', '3', '5', '7', '9']
trunc_primes = [23]
k = 2
while len(trunc_primes) < 11:
all_candidates = [int(''.join(p)) for p in product(perms, repeat = k)]
all_candidates = [j for j in all_candidates if fns.is_prime(j) == True]
for i in all_candidates:
all_facts = [str(i)[:j] for j in range(1, len(str(i)))]
all_facts = [str(i)[j:] for j in range(1, len(str(i)))] + all_facts
all_prime = all([fns.is_prime(int(j)) for j in all_facts])
if all_prime: trunc_primes.append(i)
k = k + 1
print "Euler 37:", sum(trunc_primes),
print "T:", time.time() - start; start = time.time()
# bin-dec palindromes
nmax = 1000000; all_pal = []
def is_palindrome(x):
def find_odd_comps(nmax):
all_comps = []
for i in xrange(3, nmax, 2):
if(not fns.is_prime(i)):
all_comps.append(i)
return all_comps
import fnsEuler as fns
import pandas
import numpy as np
import itertools as it
from itertools import product
import time
import math
from collections import Counter
start = time.time()
# Longest list of primes
nmax = 1000000
primes = [2] + [x for x in xrange(3, nmax/int(math.log(nmax)), 2) if fns.is_prime(x)]
max_length = 0
for i in xrange(len(primes)):
for j in xrange(i, len(primes)):
current_sum = sum(primes[i:j])
if current_sum > nmax: break
current_length = j - i
if max_length >= current_length: continue
if fns.is_prime(current_sum) and current_length > max_length:
max_length = current_length
max_sum = current_sum
print "Euler 50:", max_sum,
print "T:", time.time() - start; start = time.time()
# 28. Number diagonals
n = 501
tot = 1
current_set = [1]
for i in range(2, n+1):
current_set = range(current_set[-1] + 2 * (i-1), current_set[-1] + (2 * (i-1)) * 5, 2 * (i-1))
tot += sum(current_set)
print "Euler 28:", tot,
print "T:", time.time() - start; start = time.time()
# 27. Quadratic primes
amax = bmax = 999
b_series = [i for i in range(-amax, amax, 2) if fns.is_prime(abs(i))]
nmax = 0; best_team = [0, 0]
for a in range(-bmax, bmax, 2):
for b in b_series:
n = 0
while (fns.is_prime(abs(n * n + a * n + b))):
if n > nmax:
nmax = n
best_team = [a, b, n]
n += 1
print "Euler 27:", best_team, best_team[0] * best_team[1],
print "T:", time.time() - start; start = time.time()
# 30. Fifth digit powers
def is_prime_couple(a, b):
if fns.is_prime(int(str(a) + str(b))) and fns.is_prime(int(str(b) + str(a))):
return True
return False
import fnsEuler as fns
import numpy as np
import itertools as it
from itertools import product
import time
import math
from collections import Counter
import sys
start = time.time()
# Prime pair sets
nmax = 10000
primes_list = [x for x in xrange(1, nmax, 2) if fns.is_prime(x)]
primes_set = set(primes_list)
def is_prime_couple(a, b):
if fns.is_prime(int(str(a) + str(b))) and fns.is_prime(int(str(b) + str(a))):
return True
return False
prime_pair_hash = {}
for p in primes_set:
current_set = set()
for p1 in primes_set:
if p1 < p: continue
if is_prime_couple(p, p1):
current_set.add(p1)
prime_pair_hash[p] = current_set
