Updates README to include running time.

Work on primes to be performed. dump has been created to avoid recalculation each time.
But I 'll spend some time working on sieves.

Signed-off-by: Julien Lengrand-Lambert <julien@lengrand.fr>

README.markdown

@@ -13,35 +13,35 @@ The script are named as e_problemnumber_inc. The higher the inc, the finer my so
 Here is a list of all already solved problems, with a one line explanation. 
 Should be used in order to help future reuse of code :)
 
-1 - Add all the natural numbers below one thousand that are multiples of 3 or 5.
-2 - By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
-3 - Find the largest prime factor of a composite number.
-4 - Find the largest palindrome made from the product of two 3-digit numbers.
-5 - What is the smallest number divisible by each of the numbers 1 to 20?
-6 - What is the difference between the sum of the squares and the square of the sums?
-7 - Find the 10001st prime.
-8 - Discover the largest product of five consecutive digits in the 1000-digit number.
-9 - Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. (a^2 + b^2 = c^2)
-10 - Calculate the sum of all the primes below two million.
-11 - What is the greatest product of four adjacent numbers on the same straight line in the 20 by 20 grid?
-12 - What is the value of the first triangle number to have over five hundred divisors?
-13 - Find the first ten digits of the sum of one-hundred 50-digit numbers.
-14 - Find the longest sequence using a starting number under one million.
-15 - Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?
-16 - What is the sum of the digits of the number 2^1000?
-17 - How many letters would be needed to write all the numbers in words from 1 to 1000?
-18 - Find the maximum sum travelling from the top of the triangle to the base.
-19 - How many Sundays fell on the first of the month during the twentieth century?
-20 - Find the sum of digits in 100!
-21 - Evaluate the sum of all amicable pairs under 10000. (d(a) = b, d(b) = a)
-22 - What is the total of all the name scores in the file of first names?
-23 - Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
-24 - What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
-25 - What is the first term in the Fibonacci sequence to contain 1000 digits?
-27 - Find a quadratic formula that produces the maximum number of primes for consecutive values of n.
-36 - Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2.
-48 - Find the last ten digits of 1^1 + 2^2 + ... + 1000^1000.
-67 - Using an efficient algorithm find the maximal sum in the triangle?
+1 - Add all the natural numbers below one thousand that are multiples of 3 or 5. - 0.011
+2 - By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms. - 0.011
+3 - Find the largest prime factor of a composite number. - too long - 
+4 - Find the largest palindrome made from the product of two 3-digit numbers. - 0.790
+5 - What is the smallest number divisible by each of the numbers 1 to 20? - 4.102
+6 - What is the difference between the sum of the squares and the square of the sums? - 0.013
+7 - Find the 10001st prime. - too long - 
+8 - Discover the largest product of five consecutive digits in the 1000-digit number. - 0.045
+9 - Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. (a^2 + b^2 = c^2) - 1.500
+10 - Calculate the sum of all the primes below two million. - too long
+11 - What is the greatest product of four adjacent numbers on the same straight line in the 20 by 20 grid? - 0.048
+12 - What is the value of the first triangle number to have over five hundred divisors? - too long
+13 - Find the first ten digits of the sum of one-hundred 50-digit numbers. - 0.012
+14 - Find the longest sequence using a starting number under one million. - too long
+15 - Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner? - 0.012
+16 - What is the sum of the digits of the number 2^1000? - 0.012
+17 - How many letters would be needed to write all the numbers in words from 1 to 1000? - 0.012
+18 - Find the maximum sum travelling from the top of the triangle to the base. - 0.012
+19 - How many Sundays fell on the first of the month during the twentieth century? - 0.088
+20 - Find the sum of digits in 100! - 0.031
+21 - Evaluate the sum of all amicable pairs under 10000. (d(a) = b, d(b) = a) - 9.100
+22 - What is the total of all the name scores in the file of first names? - 0.082
+23 - Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers. - too long
+24 - What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? - too long
+25 - What is the first term in the Fibonacci sequence to contain 1000 digits? - 0.741
+27 - Find a quadratic formula that produces the maximum number of primes for consecutive values of n. - too long
+36 - Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2. - 0.933
+48 - Find the last ten digits of 1^1 + 2^2 + ... + 1000^1000. - 0.053
+67 - Using an efficient algorithm find the maximal sum in the triangle? - 0.027
 
 **In progress: **
 

e_19.py

@@ -159,4 +159,3 @@ if __name__ == '__main__' :
     start_date = Date(1901, 1, 1)
     end_date = Date(2000, 12, 31)
     print "Answer is : %d" %(days_in_period("sunday", 1, start_date, end_date))
-    raw_input() # USed to keep Windows terminal open

e_24.py

@@ -34,6 +34,4 @@ def all_permutations(seq):
         return temp
  
 if __name__ == '__main__' :
-    lexi_perm("012", 1)
-    #print "Answer is : %d" %(lexi_perm("0123456789", 1000000))
-    raw_input() # USed to keep Windows terminal open
+    print "Answer is : %d" %(lexi_perm("0123456789", 1000000))

e_36.py

@@ -41,4 +41,3 @@ def sum_palindroms(max):
     
 if __name__ == '__main__' :
     print "Answer is : %d"  % (sum_palindroms(1000000))
-    raw_input()

primes_list.py

@@ -0,0 +1,50 @@
+#!/usr/bin/env python
+"""
+ ##---
+ # Julien Lengrand-Lambert
+ #Created on : Thu Jan 19 10:12:06 CET 2012
+ #
+ # DESCRIPTION : Puts the list of all primes below one million in a file. 
+ Seeing the number of problems using primes, this could be useful
+ ##---
+ """ 
+import pickle
+
+def is_prime(value):
+    """
+    Returns True or False depending whether value is prime or not. 
+    """
+    start = 2
+    while (start <= value / 2):
+        if value % start == 0 :
+            return False
+        else : 
+            start += 1
+    return True
+    
+def prime_list(max_val):
+    """
+    Returns a list of all primes below max_val
+    """
+    plist = []
+    cur = 2
+    while (cur < max_val):
+        if (cur % 1000) == 0:    
+            print "%d/%d" % (cur, max_val)
+            
+        if (is_prime(cur)):
+            plist.append(cur)
+        cur += 1
+        
+    return plist
+ 
+if __name__ == '__main__' :
+    if 0: # creating file
+        plist = prime_list(1000000)
+        # dumping into primes_list.dump
+        pickle.dump(plist, open("primes_list.dup", "wb"))
+    else: # reading and using file
+        plist = pickle.load(open("primes_list.dup", "rb"))
+        print plist[0:100]
+        raw_input()
+    print "Done!"