Initial commit, first 27 tasks

diff --git a/.gitignore b/.gitignore
new file mode 100644 (file)
index 0000000..1f18e43
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,59 @@
+*.gem
+*.rbc
+/.config
+/coverage/
+/InstalledFiles
+/pkg/
+/spec/reports/
+/spec/examples.txt
+/test/tmp/
+/test/version_tmp/
+/tmp/
+
+# Used by dotenv library to load environment variables.
+# .env
+
+## Specific to RubyMotion:
+.dat*
+.repl_history
+build/
+*.bridgesupport
+build-iPhoneOS/
+build-iPhoneSimulator/
+
+## Specific to RubyMotion (use of CocoaPods):
+#
+# We recommend against adding the Pods directory to your .gitignore. However
+# you should judge for yourself, the pros and cons are mentioned at:
+# https://guides.cocoapods.org/using/using-cocoapods.html#should-i-check-the-pods-directory-into-source-control
+#
+# vendor/Pods/
+
+## Documentation cache and generated files:
+/.yardoc/
+/_yardoc/
+/doc/
+/rdoc/
+
+## Environment normalization:
+/.bundle/
+/vendor/bundle
+/lib/bundler/man/
+
+# for a library or gem, you might want to ignore these files since the code is
+# intended to run in multiple environments; otherwise, check them in:
+# Gemfile.lock
+# .ruby-version
+# .ruby-gemset
+
+# unless supporting rvm < 1.11.0 or doing something fancy, ignore this:
+.rvmrc
+
+# IPython
+.ipynb*
+
+# Sublime text
+*.sublime-workspace
+
+# Logs
+*.log

diff --git a/Gemfile b/Gemfile
new file mode 100644 (file)
index 0000000..209778e
--- /dev/null
+++ b/Gemfile
@@ -0,0 +1,14 @@
+# A sample Gemfile
+source "https://rubygems.org"
+
+# gem "rails"
+gem "iruby"
+gem 'rbczmq'
+# gem 'cztop'
+gem 'ffi'
+gem 'pry'
+gem 'nyaplot'
+gem 'gnuplot'
+gem 'awesome_print'
+gem 'rubyvis'
+

diff --git a/Gemfile.lock b/Gemfile.lock
new file mode 100644 (file)
index 0000000..40574db
--- /dev/null
+++ b/Gemfile.lock
@@ -0,0 +1,41 @@
+GEM
+  remote: https://rubygems.org/
+  specs:
+    awesome_print (1.7.0)
+    bond (0.5.1)
+    coderay (1.1.0)
+    data_uri (0.1.0)
+    ffi (1.9.17)
+    gnuplot (2.6.2)
+    iruby (0.2.9)
+      bond (~> 0.5)
+      data_uri (~> 0.1)
+      mimemagic (~> 0.3)
+      multi_json (~> 1.11)
+    method_source (0.8.2)
+    mimemagic (0.3.0)
+    multi_json (1.11.2)
+    nyaplot (0.1.6)
+    pry (0.10.4)
+      coderay (~> 1.1.0)
+      method_source (~> 0.8.1)
+      slop (~> 3.4)
+    rbczmq (1.7.9)
+    rubyvis (0.6.1)
+    slop (3.6.0)
+
+PLATFORMS
+  ruby
+
+DEPENDENCIES
+  awesome_print
+  ffi
+  gnuplot
+  iruby
+  nyaplot
+  pry
+  rbczmq
+  rubyvis
+
+BUNDLED WITH
+   1.10.6

diff --git a/divisors.rb b/divisors.rb
new file mode 100644 (file)
index 0000000..2ad9872
--- /dev/null
+++ b/divisors.rb
@@ -0,0 +1,53 @@
+load 'primes.rb'
+
+
+class Integer
+  # Returns a Hash of prime factors of self. 
+  # Each key is a prime factor of self, and factors[i] is the power of that prime factor
+  # For example 45.prime_factors # => {3 => 2, 5 => 1}
+  #   or, 45 = 3 ** 2 * 5 ** 1
+  def prime_factors
+    primes = Primes.instance
+    n = self
+    factors = Hash.new(0)
+    i = 0
+    while n > 1
+      if n % primes[i] == 0
+        factors[primes[i]] += 1
+        n = n.div primes[i]
+      else
+        i += 1
+      end
+    end
+    factors
+  end
+
+  def number_of_divisors
+    factors = prime_factors
+    factors.keys.reduce(1) {|a, factor| a *= factors[factor] + 1}
+  end
+
+  def sum_of_divisors
+    factors = prime_factors
+    factors.keys.map {|f|
+      (0..factors[f]).map {|a| f ** a}.reduce(:+)
+      }.reduce(:*)
+  end
+
+  def sum_of_proper_divisors
+    sum_of_divisors - self
+  end
+  
+  def perfect?
+    sum_of_proper_divisors == self
+  end
+  
+  def abundant?
+    sum_of_proper_divisors > self
+  end  
+  
+  def deficient?
+    sum_of_proper_divisors < self
+  end 
+  
+end
\ No newline at end of file

diff --git a/euler-3.rb b/euler-3.rb
new file mode 100644 (file)
index 0000000..032c8b0
--- /dev/null
+++ b/euler-3.rb
@@ -0,0 +1,30 @@
+#!/usr/bin/ruby -w
+
+require 'primes.rb'
+
+if ARGV[0].to_i != 0
+  $TARGET = ARGV[0].to_i
+else
+  $TARGET = 600851475143
+end
+
+primes = Primes.instance
+
+quotient = $TARGET
+prime_factors = []
+prime_index = 0
+
+while quotient > 1 
+# puts "trying factor #{primes[prime_index]} with quotient #{quotient}"
+  if (quotient % primes[prime_index]) == 0
+    prime_factors << primes[prime_index]
+    quotient = quotient.div primes[prime_index]
+  else
+    prime_index += 1
+  end
+end
+
+if __FILE__==$0
+  puts "Prime factors of #{$TARGET} are #{prime_factors.join(', ')}; largest is #{prime_factors.max}"
+end
+

diff --git a/euler-4-old.rb b/euler-4-old.rb
new file mode 100644 (file)
index 0000000..13d0bd6
--- /dev/null
+++ b/euler-4-old.rb
@@ -0,0 +1,37 @@
+num = 1
+dem = 1
+
+directions = [:left, :back, :down, :forward]
+
+direction = :left
+
+10.times do
+  puts "#{num}/#{dem}, dir = #{direction}"
+  case direction
+  when :left
+    num += 1
+    direction = :back
+  when :down
+    dem += 1
+    direction = :forward
+  when :back
+    if num > 1
+      num -= 1
+    else
+      direction = :forward
+    end
+    dem += 1
+  when :forward
+    if dem > 1
+      dem -= 1
+    else
+      direction = :back
+    end
+    num += 1
+  end
+end
+
+
+
+
+

diff --git a/euler-4.rb b/euler-4.rb
new file mode 100644 (file)
index 0000000..f01636f
--- /dev/null
+++ b/euler-4.rb
@@ -0,0 +1,49 @@
+ 
+def is_palindrome?(n)
+  n.to_s == n.to_s.reverse
+end
+
+
+a = b = limit = 999
+
+directions = [:left, :back, :down, :forward]
+
+direction = :left
+
+puts "#{a}/#{b}, product = #{a*b}, dir = #{direction}"
+
+while not is_palindrome?(a * b) do
+  case direction
+  when :left
+    a -= 1
+    direction = :back
+  when :down
+    b -= 1
+    direction = :forward
+  when :back
+    if a < limit
+      a += 1
+    else
+      direction = :forward
+    end
+    b -= 1
+  when :forward
+    if b < limit 
+      b += 1
+    else
+      direction = :back
+    end
+    a -= 1
+  end
+# puts "#{a}/#{b}, product = #{a*b}, dir = #{direction}"
+  end
+
+if __FILE__==$0  
+  puts "Largest palindrome is #{a*b}, the product of #{a} and #{b}"
+end
+
+
+
+
+
+

diff --git a/euler11.rb b/euler11.rb
new file mode 100644 (file)
index 0000000..b36d9bd
--- /dev/null
+++ b/euler11.rb
@@ -0,0 +1,90 @@
+grid_line = %w{ 
+08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
+49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
+81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
+52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
+22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
+24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
+32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
+67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
+24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
+21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
+78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
+16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
+86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
+19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
+04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
+88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
+04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
+20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
+20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
+01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48 }
+
+$grid = []
+grid_line.map {|s| s.to_i}.each_slice(20) {|s| $grid << s}
+$line_length = 4
+
+def find_largest_product
+  largest = 0
+  largest_row = 0
+  largest_column = 0
+  largest_direction = :east
+  $grid.length.times do |row|
+    $grid[0].length.times do |column|
+      [:east, :south_east, :south, :south_west].each do |direction|
+        this_product = find_product($grid, row, column, direction, $line_length)
+        if this_product > largest
+          largest = this_product
+          largest_row = row
+          largest_column = column
+          largest_direction = direction
+        end
+      end
+    end
+  end
+  return largest, largest_row, largest_column, largest_direction
+end
+
+def offsets_of_direction(direction)
+  case direction
+  when :north
+    return -1, 0
+  when :south
+    return 1, 0
+  when :east
+    return 0, 1
+  when :west
+    return 0, -1
+  when :north_east
+    return -1, 1
+  when :south_east
+    return 1, 1
+  when :south_west
+    return 1, -1
+  when :north_west
+    return -1, -1
+  end
+end
+
+def find_product(grid, row, column, direction, line_length)
+  row_change, column_change = offsets_of_direction(direction)
+  end_row = row + row_change * (line_length - 1)
+  end_column = column + column_change * (line_length - 1)
+  return 0 unless (0...grid.length).include? end_row and 
+    (0...grid[0].length).include? end_column
+  if row_change == 0
+    rows = [row] * line_length
+  else
+    rows = row.step(end_row, row_change).to_a
+  end
+  if column_change == 0
+    cols = [column] * line_length
+  else
+    cols = column.step(end_column, column_change).to_a
+  end
+  rows.zip(cols).reduce(1) {|product, i| product *= grid[i[0]][i[1]]}
+end
+
+if __FILE__==$0
+  puts find_largest_product[0]
+end
\ No newline at end of file

diff --git a/euler12.rb b/euler12.rb
new file mode 100644 (file)
index 0000000..f6df027
--- /dev/null
+++ b/euler12.rb
@@ -0,0 +1,25 @@
+load 'divisors.rb'
+
+require 'logger'
+$log = Logger.new(STDERR)
+$log.level = Logger::WARN
+
+
+# The nth triangle number
+def triangle(n)
+  n * (n + 1) / 2
+end
+
+def first_triangle_number_with_more_than_n_divisors(n)
+  i = 1
+  while triangle(i).number_of_divisors <= 500
+    $log.info { "Triangle number #{i} is #{triangle(i)}, which has #{triangle(i).number_of_divisors} divisors" }
+    i += 1
+  end
+  $log.info { "Triangle number #{i} is #{triangle(i)}, which has #{triangle(i).number_of_divisors} divisors" }
+  triangle i
+end
+
+if __FILE__==$0
+  puts first_triangle_number_with_more_than_n_divisors(500)
+end

diff --git a/euler13.rb b/euler13.rb
new file mode 100644 (file)
index 0000000..67e600b
--- /dev/null
+++ b/euler13.rb
@@ -0,0 +1,105 @@
+$numbers = %w{
+37107287533902102798797998220837590246510135740250
+46376937677490009712648124896970078050417018260538
+74324986199524741059474233309513058123726617309629
+91942213363574161572522430563301811072406154908250
+23067588207539346171171980310421047513778063246676
+89261670696623633820136378418383684178734361726757
+28112879812849979408065481931592621691275889832738
+44274228917432520321923589422876796487670272189318
+47451445736001306439091167216856844588711603153276
+70386486105843025439939619828917593665686757934951
+62176457141856560629502157223196586755079324193331
+64906352462741904929101432445813822663347944758178
+92575867718337217661963751590579239728245598838407
+58203565325359399008402633568948830189458628227828
+80181199384826282014278194139940567587151170094390
+35398664372827112653829987240784473053190104293586
+86515506006295864861532075273371959191420517255829
+71693888707715466499115593487603532921714970056938
+54370070576826684624621495650076471787294438377604
+53282654108756828443191190634694037855217779295145
+36123272525000296071075082563815656710885258350721
+45876576172410976447339110607218265236877223636045
+17423706905851860660448207621209813287860733969412
+81142660418086830619328460811191061556940512689692
+51934325451728388641918047049293215058642563049483
+62467221648435076201727918039944693004732956340691
+15732444386908125794514089057706229429197107928209
+55037687525678773091862540744969844508330393682126
+18336384825330154686196124348767681297534375946515
+80386287592878490201521685554828717201219257766954
+78182833757993103614740356856449095527097864797581
+16726320100436897842553539920931837441497806860984
+48403098129077791799088218795327364475675590848030
+87086987551392711854517078544161852424320693150332
+59959406895756536782107074926966537676326235447210
+69793950679652694742597709739166693763042633987085
+41052684708299085211399427365734116182760315001271
+65378607361501080857009149939512557028198746004375
+35829035317434717326932123578154982629742552737307
+94953759765105305946966067683156574377167401875275
+88902802571733229619176668713819931811048770190271
+25267680276078003013678680992525463401061632866526
+36270218540497705585629946580636237993140746255962
+24074486908231174977792365466257246923322810917141
+91430288197103288597806669760892938638285025333403
+34413065578016127815921815005561868836468420090470
+23053081172816430487623791969842487255036638784583
+11487696932154902810424020138335124462181441773470
+63783299490636259666498587618221225225512486764533
+67720186971698544312419572409913959008952310058822
+95548255300263520781532296796249481641953868218774
+76085327132285723110424803456124867697064507995236
+37774242535411291684276865538926205024910326572967
+23701913275725675285653248258265463092207058596522
+29798860272258331913126375147341994889534765745501
+18495701454879288984856827726077713721403798879715
+38298203783031473527721580348144513491373226651381
+34829543829199918180278916522431027392251122869539
+40957953066405232632538044100059654939159879593635
+29746152185502371307642255121183693803580388584903
+41698116222072977186158236678424689157993532961922
+62467957194401269043877107275048102390895523597457
+23189706772547915061505504953922979530901129967519
+86188088225875314529584099251203829009407770775672
+11306739708304724483816533873502340845647058077308
+82959174767140363198008187129011875491310547126581
+97623331044818386269515456334926366572897563400500
+42846280183517070527831839425882145521227251250327
+55121603546981200581762165212827652751691296897789
+32238195734329339946437501907836945765883352399886
+75506164965184775180738168837861091527357929701337
+62177842752192623401942399639168044983993173312731
+32924185707147349566916674687634660915035914677504
+99518671430235219628894890102423325116913619626622
+73267460800591547471830798392868535206946944540724
+76841822524674417161514036427982273348055556214818
+97142617910342598647204516893989422179826088076852
+87783646182799346313767754307809363333018982642090
+10848802521674670883215120185883543223812876952786
+71329612474782464538636993009049310363619763878039
+62184073572399794223406235393808339651327408011116
+66627891981488087797941876876144230030984490851411
+60661826293682836764744779239180335110989069790714
+85786944089552990653640447425576083659976645795096
+66024396409905389607120198219976047599490197230297
+64913982680032973156037120041377903785566085089252
+16730939319872750275468906903707539413042652315011
+94809377245048795150954100921645863754710598436791
+78639167021187492431995700641917969777599028300699
+15368713711936614952811305876380278410754449733078
+40789923115535562561142322423255033685442488917353
+44889911501440648020369068063960672322193204149535
+41503128880339536053299340368006977710650566631954
+81234880673210146739058568557934581403627822703280
+82616570773948327592232845941706525094512325230608
+22918802058777319719839450180888072429661980811197
+77158542502016545090413245809786882778948721859617
+72107838435069186155435662884062257473692284509516
+20849603980134001723930671666823555245252804609722
+53503534226472524250874054075591789781264330331690 }.map {|i| i.to_i}
+
+if __FILE__==$0
+  p $numbers.reduce(:+).to_s[0..9]
+end

diff --git a/euler14.rb b/euler14.rb
new file mode 100644 (file)
index 0000000..567eac3
--- /dev/null
+++ b/euler14.rb
@@ -0,0 +1,29 @@
+require 'logger'
+log = Logger.new(STDERR)
+log.level = Logger::WARN
+
+$chain_lengths = {1 => 1}
+
+def chain_length(n)
+  unless $chain_lengths.has_key?(n)
+    if n % 2 == 0
+      $chain_lengths[n] = 1 + chain_length(n / 2)
+    else
+      $chain_lengths[n] = 1 + chain_length(3 * n + 1)
+    end
+  end
+  $chain_lengths[n]
+end
+
+longest_chain_start = 1
+1.upto(1000000) do |i|
+  if chain_length(i) > chain_length(longest_chain_start)
+    longest_chain_start = i
+    log.info {"Found new longest chain. Starts at #{i}, #{chain_length(i)} elements"}
+  end
+  log.debug {"#{i} has chain length #{chain_length(i)}"}
+end
+
+puts "Longest chain starts at #{longest_chain_start}, with #{$chain_lengths[longest_chain_start]} elements"
+
+log.close
\ No newline at end of file

diff --git a/euler14.sb b/euler14.sb
new file mode 100644 (file)
index 0000000..8bfb83e
Binary files /dev/null and b/euler14.sb differ

diff --git a/euler15.rb b/euler15.rb
new file mode 100644 (file)
index 0000000..117e230
--- /dev/null
+++ b/euler15.rb
@@ -0,0 +1,9 @@
+class Integer
+  def factorial
+    Array.new(self) {|i| i + 1}.reduce(:*)
+  end
+end
+
+if __FILE__==$0
+  print 40.factorial / (20.factorial ** 2)
+end

diff --git a/euler16.rb b/euler16.rb
new file mode 100644 (file)
index 0000000..5c6d2e9
--- /dev/null
+++ b/euler16.rb
@@ -0,0 +1,3 @@
+if __FILE__==$0
+  p (2 ** 1000).to_s.scan(/./).map{|d| d.to_i}.reduce(:+)
+end
\ No newline at end of file

diff --git a/euler17.rb b/euler17.rb
new file mode 100644 (file)
index 0000000..dd1554b
--- /dev/null
+++ b/euler17.rb
@@ -0,0 +1,58 @@
+require 'logger'
+log = Logger.new(STDERR)
+log.level = Logger::WARN
+
+$words = {1 => 'one',
+          2 => 'two',
+          3 => 'three',
+          4 => 'four',
+          5 => 'five',
+          6 => 'six',
+          7 => 'seven',
+          8 => 'eight',
+          9 => 'nine',
+         10 => 'ten',
+         11 => 'eleven',
+         12 => 'twelve',
+         13 => 'thirteen',
+         14 => 'fourteen',
+         15 => 'fifteen',
+         16 => 'sixteen',
+         17 => 'seventeen',
+         18 => 'eighteen',
+         19 => 'nineteen',
+         20 => 'twenty',
+         30 => 'thirty',
+         40 => 'forty',
+         50 => 'fifty',
+         60 => 'sixty',
+         70 => 'seventy',
+         80 => 'eighty',
+         90 => 'ninety',
+        100 => 'hundred',
+       1000 => 'thousand'}
+
+def words_of_number(n)
+  case n
+  when (1..20)
+    [$words[n]]
+  when (21..99)
+    [$words[n.div(10) * 10], $words[n % 10]]
+  when (100..999)
+    [$words[n.div(100)], 'hundred'] + (n % 100 == 0 ? [] : ['and'] + words_of_number(n % 100))
+  when 1000
+    ['one', 'thousand']
+  end
+end
+
+if __FILE__==$0
+  words = []
+  1.upto(1000) do |i|
+    words += words_of_number(i)
+    log.info { "Number #{i} gives words #{words_of_number i}" }
+  end
+
+  puts words.join('').length
+end
+
+log.close
\ No newline at end of file

diff --git a/euler18.rb b/euler18.rb
new file mode 100644 (file)
index 0000000..8bfb065
--- /dev/null
+++ b/euler18.rb
@@ -0,0 +1,44 @@
+require 'logger'
+
+$triangle_source = <<TRIANGLE   
+75
+95 64
+17 47 82
+18 35 87 10
+20 04 82 47 65
+19 01 23 75 03 34
+88 02 77 73 07 63 67
+99 65 04 28 06 16 70 92
+41 41 26 56 83 40 80 70 33
+41 48 72 33 47 32 37 16 94 29
+53 71 44 65 25 43 91 52 97 51 14
+70 11 33 28 77 73 17 78 39 68 17 57
+91 71 52 38 17 14 91 43 58 50 27 29 48
+63 66 04 68 89 53 67 30 73 16 69 87 40 31
+04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
+TRIANGLE
+
+$triangle = $triangle_source.split("\n").map {|line| line.split.map {|s| s.to_i}}
+
+def find_best(triangle)
+  log = Logger.new(STDERR)
+  log.level = Logger::WARN
+  last_line_totals = [0]
+  this_line_totals = []
+  triangle.each do |line|
+    log.info {"Checking line #{line}"}
+    this_line_totals = []
+    line.each_index do |i|
+      this_line_totals << [i == 0 ? 0 : last_line_totals[i-1] + line[i], 
+                           i == last_line_totals.length ? 0 : last_line_totals[i] + line[i]].max
+    end
+    log.info {"Best totals for line #{line} are #{this_line_totals}"}
+    last_line_totals = this_line_totals
+  end
+  log.close
+  this_line_totals.max
+end
+
+if __FILE__==$0
+  puts find_best $triangle
+end
\ No newline at end of file

diff --git a/euler19.rb b/euler19.rb
new file mode 100644 (file)
index 0000000..a984050
--- /dev/null
+++ b/euler19.rb
@@ -0,0 +1,19 @@
+require 'date'
+require 'logger'
+log = Logger.new(STDERR)
+log.level = Logger::WARN
+
+sundays = 0
+1901.upto(2000) do |year|
+  1.upto(12) do |month|
+    sundays += 1 if Date.new(year, month, 1).sunday?
+    log.debug { "#{Date.new(year, month, 1)} is daynum #{Date.new(year, month, 1).cwday}"}
+    log.info { "#{Date.new(year, month, 1)} is a sunday, making #{sundays} so far" } if Date.new(year, month, 1).sunday?
+  end
+end
+
+if __FILE__==$0
+  puts sundays
+end
+
+log.close
\ No newline at end of file

diff --git a/euler20.rb b/euler20.rb
new file mode 100644 (file)
index 0000000..3818a79
--- /dev/null
+++ b/euler20.rb
@@ -0,0 +1,9 @@
+class Integer
+  def factorial
+    Array.new(self) {|i| i + 1}.reduce(:*)
+  end
+end
+
+if __FILE__==$0
+  puts 100.factorial.to_s.scan(/./).map{|s| s.to_i}.reduce(:+)
+end
\ No newline at end of file

diff --git a/euler21.rb b/euler21.rb
new file mode 100644 (file)
index 0000000..4adec38
--- /dev/null
+++ b/euler21.rb
@@ -0,0 +1,32 @@
+load 'primes.rb'
+load 'divisors.rb'
+
+require 'logger'
+$log = Logger.new(STDERR)
+$log.level = Logger::WARN
+
+def amicable_pairs(limit)
+  cache = [0,0]
+  2.upto(limit) do |n|
+    cache << n.sum_of_proper_divisors
+    $log.debug { "Sum of proper divisors of #{n} is #{n.sum_of_proper_divisors}" }
+  end
+  amicable_pairs = []
+  2.upto(limit) do |n|
+    if cache[cache[n]] == n and cache[n] > n
+      amicable_pairs << [n, cache[n]] 
+      $log.info { "Found amicable pairs #{n} and #{cache[n]}" }
+    end
+  end
+  amicable_pairs
+end
+
+def sum_of_amicable_pairs(limit)
+  amicable_pairs(limit).reduce(0) {|a, p| a += p.reduce(:+)}
+end
+
+if __FILE__==$0
+  puts sum_of_amicable_pairs 10000
+end
+
+log.close
\ No newline at end of file

diff --git a/euler22-names.txt b/euler22-names.txt
new file mode 100644 (file)
index 0000000..7b8986b
--- /dev/null
+++ b/euler22-names.txt
@@ -0,0 +1 @@
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","BERTRAM","MARKUS","HUEY","HILTON","DWAIN","DONTE","TYRON","OMER","ISAIAS","HIPOLITO","FERMIN","ADALBERTO","BO","BARRETT","TEODORO","MCKINLEY","MAXIMO","GARFIELD","RALEIGH","LAWERENCE","ABRAM","RASHAD","KING","EMMITT","DARON","SAMUAL","MIQUEL","EUSEBIO","DOMENIC","DARRON","BUSTER","WILBER","RENATO","JC","HOYT","HAYWOOD","EZEKIEL","CHAS","FLORENTINO","ELROY","CLEMENTE","ARDEN","NEVILLE","EDISON","DESHAWN","NATHANIAL","JORDON","DANILO","CLAUD","SHERWOOD","RAYMON","RAYFORD","CRISTOBAL","AMBROSE","TITUS","HYMAN","FELTON","EZEQUIEL","ERASMO","STANTON","LONNY","LEN","IKE","MILAN","LINO","JAROD","HERB","ANDREAS","WALTON","RHETT","PALMER","DOUGLASS","CORDELL","OSWALDO","ELLSWORTH","VIRGILIO","TONEY","NATHANAEL","DEL","BENEDICT","MOSE","JOHNSON","ISREAL","GARRET","FAUSTO","ASA","ARLEN","ZACK","WARNER","MODESTO","FRANCESCO","MANUAL","GAYLORD","GASTON","FILIBERTO","DEANGELO","MICHALE","GRANVILLE","WES","MALIK","ZACKARY","TUAN","ELDRIDGE","CRISTOPHER","CORTEZ","ANTIONE","MALCOM","LONG","KOREY","JOSPEH","COLTON","WAYLON","VON","HOSEA","SHAD","SANTO","RUDOLF","ROLF","REY","RENALDO","MARCELLUS","LUCIUS","KRISTOFER","BOYCE","BENTON","HAYDEN","HARLAND","ARNOLDO","RUEBEN","LEANDRO","KRAIG","JERRELL","JEROMY","HOBERT","CEDRICK","ARLIE","WINFORD","WALLY","LUIGI","KENETH","JACINTO","GRAIG","FRANKLYN","EDMUNDO","SID","PORTER","LEIF","JERAMY","BUCK","WILLIAN","VINCENZO","SHON","LYNWOOD","JERE","HAI","ELDEN","DORSEY","DARELL","BRODERICK","ALONSO"
\ No newline at end of file

diff --git a/euler22.rb b/euler22.rb
new file mode 100644 (file)
index 0000000..23f7cc3
--- /dev/null
+++ b/euler22.rb
@@ -0,0 +1,23 @@
+require 'logger'
+$log = Logger.new(STDERR)
+$log.level = Logger::WARN
+
+def value_of_char(char)
+  char.ord - "A".ord + 1
+end
+
+def value_of_word(word)
+  word.scan(/./).map{|c| value_of_char c}.reduce(:+)
+end
+
+if __FILE__==$0
+  total = 0
+  $names = File.read('euler22-names.txt').strip.slice(1..-2).split('","').sort
+  $names.each_index do |i|
+    total += (i + 1) * value_of_word($names[i])
+  end
+
+  puts total
+end
+
+$log.close
\ No newline at end of file

diff --git a/euler23.rb b/euler23.rb
new file mode 100644 (file)
index 0000000..9eaf8cb
--- /dev/null
+++ b/euler23.rb
@@ -0,0 +1,24 @@
+load 'divisors.rb'
+
+require 'logger'
+$log = Logger.new(STDERR)
+$log.level = Logger::WARN
+
+abundant_numbers = (12..28124).select {|i| i.abundant?}
+
+candidates = Array.new(28124) {|i| i}
+candidates[0] = nil
+
+abundant_numbers.each_index do |i|
+  j = abundant_numbers.length - 1
+  while j >= i
+    candidates[abundant_numbers[i] + abundant_numbers[j]] = nil
+    $log.info {"Eliminating #{abundant_numbers[i] + abundant_numbers[j]} as the sum of #{abundant_numbers[i]} and #{abundant_numbers[j]} (i=#{i}, j=#{j})" }
+    j -= 1
+  end
+end
+
+# p candidates.compact
+p candidates.compact.reduce(:+)
+
+$log.close
\ No newline at end of file

diff --git a/euler24.rb b/euler24.rb
new file mode 100644 (file)
index 0000000..0621de5
--- /dev/null
+++ b/euler24.rb
@@ -0,0 +1,54 @@
+require 'logger'
+$log = Logger.new(STDERR)
+$log.level = Logger::WARN
+
+
+class Integer
+  def to_factorial_radix
+    return [0] if self == 0
+    remainder = self
+    result = []
+    radix = 1
+    while remainder > 0
+      result << (remainder % radix)
+      remainder = remainder.div radix
+      radix += 1
+    end
+    result.reverse
+  end
+end
+
+class Array
+  def factorial_radix_to_i(current_radix = 0)
+    $log.info { "Calling factorial_radix_to_i with string #{self} and current_radix = #{current_radix}" }
+    return 0 if self.empty?
+    return 0 if self == [0]
+    value_of_rest = self[0..-2].factorial_radix_to_i(current_radix + 1)
+    $log.info { "Value of remainder = #{value_of_rest}" }
+    $log.info { "Returning #{self[-1] + value_of_rest}" }
+    self[-1] + (current_radix + 1) * value_of_rest
+  end
+  
+  def prepad_with_zeros(length)
+    [0] * [length - self.length, 0].max + self
+  end
+  
+  def permutation_from_factorial_radix_number(n)
+    $log.info { "Permuting #{self} with frn #{n}" }
+    return [] if n.empty?
+    return self if self.empty?
+    items_copy = self.dup
+    permutation = [items_copy.delete_at(n[0])]
+    permutation += items_copy.permutation_from_factorial_radix_number(n[1..-1])
+  end
+  
+  def nth_permutation(n)
+    permutation_from_factorial_radix_number(n.to_factorial_radix.prepad_with_zeros(self.length))
+  end
+end
+
+if __FILE__==$0
+  puts (Array.new(10) {|i| i}).nth_permutation(10 ** 6 - 1).join('')
+end
+
+$log.close
\ No newline at end of file

diff --git a/euler25.rb b/euler25.rb
new file mode 100644 (file)
index 0000000..9fa8b30
--- /dev/null
+++ b/euler25.rb
@@ -0,0 +1,9 @@
+load 'fibonacci.rb'
+
+i = 100
+while i.fibonacci.to_s.length < 1000
+  i += 1
+end
+
+puts "The #{i}th Fibonacci term has #{i.fibonacci.to_s.length} digits"
+puts "The previous, #{i-1}th Fibonacci term has #{(i-1).fibonacci.to_s.length} digits"

diff --git a/euler26.ipynb b/euler26.ipynb
new file mode 100644 (file)
index 0000000..0b25dd6
--- /dev/null
+++ b/euler26.ipynb
@@ -0,0 +1,368 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "true"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "require \"awesome_print\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":division"
+      ]
+     },
+     "execution_count": 91,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def division(n, debug: false)\n",
+    "  dividend = 10\n",
+    "  divisor = n\n",
+    "  quotient = \"0.\"\n",
+    "  trail = []\n",
+    "  while dividend != 0 && !(trail.include?(dividend))\n",
+    "    q, r = dividend.divmod(divisor)\n",
+    "    puts(\"#{dividend} #{divisor} #{q} #{r} #{!(trail.include?(dividend))} #{trail}\") if debug\n",
+    "    if q == 0\n",
+    "      dividend *= 10\n",
+    "      quotient += \"0\"\n",
+    "      trail += [0]\n",
+    "    else\n",
+    "      trail += [dividend]\n",
+    "      quotient += q.to_s\n",
+    "      dividend = r * 10\n",
+    "    end\n",
+    "  end\n",
+    "  if dividend != 0\n",
+    "    cycle_length = trail.length - trail.rindex(dividend)\n",
+    "  else\n",
+    "    cycle_length = 0\n",
+    "  end\n",
+    "  # return quotient, cycle_length, trail + [dividend]\n",
+    "  cycle_length\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[0, 1]"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "q, r = 1.divmod(8)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[1, 2]"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "q, r = 10.divmod(8)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2, 4]"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "q, r = 20.divmod(8)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[5, 0]"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "q, r = 40.divmod(8)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 92,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "division(8)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 93,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "division(7)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 94,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "division(3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2: 0\n",
+      "3: 1\n",
+      "4: 0\n",
+      "5: 0\n",
+      "6: 1\n",
+      "7: 6\n",
+      "8: 0\n",
+      "9: 1\n",
+      "10: 0\n",
+      "11: 2\n",
+      "12: 1\n",
+      "13: 6\n",
+      "14: 6\n",
+      "15: 1\n",
+      "16: 0\n",
+      "17: 16\n",
+      "18: 1\n",
+      "19: 18\n",
+      "20: 0\n",
+      "21: 6\n",
+      "22: 2\n",
+      "23: 22\n",
+      "24: 1\n",
+      "25: 0\n",
+      "26: 6\n",
+      "27: 3\n",
+      "28: 6\n",
+      "29: 28\n",
+      "30: 1\n",
+      "31: 15\n",
+      "32: 0\n",
+      "33: 2\n",
+      "34: 16\n",
+      "35: 6\n",
+      "36: 1\n",
+      "37: 3\n",
+      "38: 18\n",
+      "39: 6\n",
+      "40: 0\n",
+      "41: 5\n",
+      "42: 6\n",
+      "43: 21\n",
+      "44: 2\n",
+      "45: 1\n",
+      "46: 22\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "2..46"
+      ]
+     },
+     "execution_count": 95,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(2..46).each do |i| puts(\"#{i}: #{division(i)}\") end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 99,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "983"
+      ]
+     },
+     "execution_count": 99,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(1..1000).max_by {|i| division(i)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 97,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "division(1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Ruby 2.4.0",
+   "language": "ruby",
+   "name": "ruby"
+  },
+  "language_info": {
+   "file_extension": ".rb",
+   "mimetype": "application/x-ruby",
+   "name": "ruby",
+   "version": "2.4.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}

diff --git a/euler27.ipynb b/euler27.ipynb
new file mode 100644 (file)
index 0000000..06084a8
--- /dev/null
+++ b/euler27.ipynb
@@ -0,0 +1,613 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "true"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "require \"awesome_print\"\n",
+    "load 'primes.rb'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "#<Primes:0x0055d434088d98 @primes=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973], @cache_up_to=30, @mod_candidates=[1, 7, 11, 13, 17, 19, 23, 29]>"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "primes = Primes.instance;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "false"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "primes.include? 10008"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 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9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009]"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "primes.primes"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: 41\n",
+      "1: 43\n",
+      "2: 47\n",
+      "3: 53\n",
+      "4: 61\n",
+      "5: 71\n",
+      "6: 83\n",
+      "7: 97\n",
+      "8: 113\n",
+      "9: 131\n",
+      "10: 151\n",
+      "11: 173\n",
+      "12: 197\n",
+      "13: 223\n",
+      "14: 251\n",
+      "15: 281\n",
+      "16: 313\n",
+      "17: 347\n",
+      "18: 383\n",
+      "19: 421\n",
+      "20: 461\n",
+      "21: 503\n",
+      "22: 547\n",
+      "23: 593\n",
+      "24: 641\n",
+      "25: 691\n",
+      "26: 743\n",
+      "27: 797\n",
+      "28: 853\n",
+      "29: 911\n",
+      "30: 971\n",
+      "31: 1033\n",
+      "32: 1097\n",
+      "33: 1163\n",
+      "34: 1231\n",
+      "35: 1301\n",
+      "36: 1373\n",
+      "37: 1447\n",
+      "38: 1523\n",
+      "39: 1601\n",
+      "40: 1681\n",
+      "41: 1763\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "42"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "42.times do |i|\n",
+    "  puts(\"#{i}: #{i**2 + i + 41}\")\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: 1601\n",
+      "1: 1523\n",
+      "2: 1447\n",
+      "3: 1373\n",
+      "4: 1301\n",
+      "5: 1231\n",
+      "6: 1163\n",
+      "7: 1097\n",
+      "8: 1033\n",
+      "9: 971\n",
+      "10: 911\n",
+      "11: 853\n",
+      "12: 797\n",
+      "13: 743\n",
+      "14: 691\n",
+      "15: 641\n",
+      "16: 593\n",
+      "17: 547\n",
+      "18: 503\n",
+      "19: 461\n",
+      "20: 421\n",
+      "21: 383\n",
+      "22: 347\n",
+      "23: 313\n",
+      "24: 281\n",
+      "25: 251\n",
+      "26: 223\n",
+      "27: 197\n",
+      "28: 173\n",
+      "29: 151\n",
+      "30: 131\n",
+      "31: 113\n",
+      "32: 97\n",
+      "33: 83\n",
+      "34: 71\n",
+      "35: 61\n",
+      "36: 53\n",
+      "37: 47\n",
+      "38: 43\n",
+      "39: 41\n",
+      "40: 41\n",
+      "41: 43\n",
+      "42: 47\n",
+      "43: 53\n",
+      "44: 61\n",
+      "45: 71\n",
+      "46: 83\n",
+      "47: 97\n",
+      "48: 113\n",
+      "49: 131\n",
+      "50: 151\n",
+      "51: 173\n",
+      "52: 197\n",
+      "53: 223\n",
+      "54: 251\n",
+      "55: 281\n",
+      "56: 313\n",
+      "57: 347\n",
+      "58: 383\n",
+      "59: 421\n",
+      "60: 461\n",
+      "61: 503\n",
+      "62: 547\n",
+      "63: 593\n",
+      "64: 641\n",
+      "65: 691\n",
+      "66: 743\n",
+      "67: 797\n",
+      "68: 853\n",
+      "69: 911\n",
+      "70: 971\n",
+      "71: 1033\n",
+      "72: 1097\n",
+      "73: 1163\n",
+      "74: 1231\n",
+      "75: 1301\n",
+      "76: 1373\n",
+      "77: 1447\n",
+      "78: 1523\n",
+      "79: 1601\n",
+      "80: 1681\n",
+      "81: 1763\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "82"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "82.times do |i|\n",
+    "  puts(\"#{i}: #{i**2 - 79* i + 1601}\")\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-9\n",
+      "-8\n",
+      "-7\n",
+      "-6\n",
+      "-5\n",
+      "-4\n",
+      "-3\n",
+      "-2\n",
+      "-1\n",
+      "0\n",
+      "1\n",
+      "2\n",
+      "3\n",
+      "4\n",
+      "5\n",
+      "6\n",
+      "7\n",
+      "8\n",
+      "9\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "-9..9"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(-9..9).each {|i| puts(i)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       ":count_primes"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def count_primes(primes, a, b)\n",
+    "  n = 0\n",
+    "  y = b\n",
+    "  count = 0\n",
+    "  while primes.include? y\n",
+    "    count += 1\n",
+    "    n += 1\n",
+    "    y = n ** 2 + a * n + b\n",
+    "  end\n",
+    "  count  \n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "40"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "count_primes(primes, 1, 41)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "80"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "count_primes(primes, -79, 1601)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
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+      ]
+     },
+     "execution_count": 33,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "coeffs = (-50..50).to_a.product((0..50).to_a);"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
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1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 0, 6, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0]"
+      ]
+     },
+     "execution_count": 34,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "coeffs.map {|a, b| count_primes(primes, a, b)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[-5, 47]"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "coeffs.max_by {|a, b| count_primes(primes, a, b)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "43"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "count_primes(primes, -5, 47)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {
+    "collapsed": false,
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: 47 true\n",
+      "1: 43 true\n",
+      "2: 41 true\n",
+      "3: 41 true\n",
+      "4: 43 true\n",
+      "5: 47 true\n",
+      "6: 53 true\n",
+      "7: 61 true\n",
+      "8: 71 true\n",
+      "9: 83 true\n",
+      "10: 97 true\n",
+      "11: 113 true\n",
+      "12: 131 true\n",
+      "13: 151 true\n",
+      "14: 173 true\n",
+      "15: 197 true\n",
+      "16: 223 true\n",
+      "17: 251 true\n",
+      "18: 281 true\n",
+      "19: 313 true\n",
+      "20: 347 true\n",
+      "21: 383 true\n",
+      "22: 421 true\n",
+      "23: 461 true\n",
+      "24: 503 true\n",
+      "25: 547 true\n",
+      "26: 593 true\n",
+      "27: 641 true\n",
+      "28: 691 true\n",
+      "29: 743 true\n",
+      "30: 797 true\n",
+      "31: 853 true\n",
+      "32: 911 true\n",
+      "33: 971 true\n",
+      "34: 1033 true\n",
+      "35: 1097 true\n",
+      "36: 1163 true\n",
+      "37: 1231 true\n",
+      "38: 1301 true\n",
+      "39: 1373 true\n",
+      "40: 1447 true\n",
+      "41: 1523 true\n",
+      "42: 1601 true\n",
+      "43: 1681 false\n",
+      "44: 1763 false\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "45"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "45.times do |i|\n",
+    "  puts(\"#{i}: #{i**2 - 5 * i + 47} #{primes.include? i**2 - 5 * i + 47}\")\n",
+    "end"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "-61, 971 : -59231\n"
+     ]
+    }
+   ],
+   "source": [
+    "coeffs = (-999..999).to_a.product((0..1000).to_a)\n",
+    "am, bm = coeffs.max_by {|a, b| count_primes(primes, a, b)}\n",
+    "puts \"#{am}, #{bm} : #{am * bm}\""
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Ruby 2.4.0",
+   "language": "ruby",
+   "name": "ruby"
+  },
+  "language_info": {
+   "file_extension": ".rb",
+   "mimetype": "application/x-ruby",
+   "name": "ruby",
+   "version": "2.4.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}

diff --git a/euler67-triangle.txt b/euler67-triangle.txt
new file mode 100644 (file)
index 0000000..00f98e3
--- /dev/null
+++ b/euler67-triangle.txt
@@ -0,0 +1,100 @@
+59\r
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diff --git a/euler67.rb b/euler67.rb
new file mode 100644 (file)
index 0000000..50a55fb
--- /dev/null
+++ b/euler67.rb
@@ -0,0 +1,26 @@
+require 'logger'
+
+$triangle = File.readlines('euler67-triangle.txt').map {|line| line.chomp.split.map {|s| s.to_i}}
+
+def find_best(triangle)
+  log = Logger.new(STDERR)
+  log.level = Logger::WARN
+  last_line_totals = [0]
+  this_line_totals = []
+  triangle.each do |line|
+    log.info {"Checking line #{line}"}
+    this_line_totals = []
+    line.each_index do |i|
+      this_line_totals << [i == 0 ? 0 : last_line_totals[i-1] + line[i], 
+                           i == last_line_totals.length ? 0 : last_line_totals[i] + line[i]].max
+    end
+    log.info {"Best totals for line #{line} are #{this_line_totals}"}
+    last_line_totals = this_line_totals
+  end
+  log.close
+  this_line_totals.max
+end
+
+if __FILE__==$0
+  puts find_best $triangle
+end

diff --git a/euler7.rb b/euler7.rb
new file mode 100644 (file)
index 0000000..f8ed868
--- /dev/null
+++ b/euler7.rb
@@ -0,0 +1,15 @@
+primes = Array.new
+
+2.upto 2000000 do |i|
+  primes << i
+end
+
+n = 0
+while primes[n] ** 2 <= primes[-1]
+
+  primes.reject! {|i| i % primes[n] == 0 and i > primes[n]}
+  n = n+1
+end
+
+puts "found#{primes.length} primes"
+puts "100th prime is #{primes[99]}"

diff --git a/fibonacci.rb b/fibonacci.rb
new file mode 100644 (file)
index 0000000..d2c55c3
--- /dev/null
+++ b/fibonacci.rb
@@ -0,0 +1,22 @@
+class Integer
+  # Return the self'th Fibonacci number
+  def fibonacci_slow
+    return self if self <= 1
+    return 1 if self == 2
+    f2 = 0 # the n-2th term
+    f1 = 1 # the n-1th term
+    f0 = 1
+    3.upto(self) do |i|
+      f0, f1, f2 = f0 + f1, f0, f1
+    end
+    f0
+  end
+  
+  @@fibonacci_cache = {0 => 0, 1 => 1, 2 => 1}
+  def fibonacci
+       unless @@fibonacci_cache.has_key?(self)
+         @@fibonacci_cache[self] = ((self - 2).fibonacci + (self - 1).fibonacci)
+       end
+       @@fibonacci_cache[self]
+  end
+end

diff --git a/primes.rb b/primes.rb
new file mode 100644 (file)
index 0000000..0febe80
--- /dev/null
+++ b/primes.rb
@@ -0,0 +1,100 @@
+# A faster Prime number library
+
+# To use:
+# require 'primes.rb'
+# primes = Primes.instance
+# primes.take(20) # returns the first 20 primes
+# primes[10000]   # returns the 10,001st prime
+
+require 'singleton'
+
+class Primes 
+  include Enumerable
+
+  attr_accessor :mod_candidates
+
+  include Singleton
+
+  def initialize(sieve_limit = 10000)
+    # @primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+    @primes = sieve sieve_limit
+    @cache_up_to = 30
+    @mod_candidates = ((1..@cache_up_to).collect {|x| x}).select {|x| [2, 3, 5].all? {|p| x % p != 0}}
+  end
+
+  def primes
+    @primes.dup
+  end
+
+  def next_prime
+    candidate = next_candidate(@primes[-1])
+    while @primes.any? {|i| candidate % i == 0 }
+      candidate = next_candidate(candidate)
+    end
+    candidate
+  end
+
+  def each &block
+    i = 0
+    while true do
+      add_next_prime! if i >= @primes.length
+      block.call @primes[i]
+      i += 1
+    end
+  end
+  
+  def next_candidate(candidate)
+    c_increments = @mod_candidates.select {|c| c > candidate % @cache_up_to}
+    if c_increments.empty?
+      next_candidate = (candidate.div(@cache_up_to) + 1) * @cache_up_to + @mod_candidates[0]
+    else
+      next_candidate = candidate.div(@cache_up_to) * @cache_up_to + c_increments.first
+    end
+    next_candidate
+  end
+
+  def add_next_prime!
+    @primes.push next_prime
+  end
+
+  # No longer needed: use Enumerable#take_while instead
+#   def primes_until
+#     add_next_prime! while not yield(@primes)
+#     @primes
+#   end
+
+  # the nth prime
+  def [](n)
+    if @primes.length <= n
+      (n - @primes.length + 1).times { add_next_prime! }
+      # primes_until {|ps| ps.length > n}
+    end
+    @primes[n]
+  end
+    
+  # Perform sieve of Eratosthenes
+  # Algorithm courtesy of Marc Seeger at http://blog.marc-seeger.de/2010/12/05/prime-numbers-in-ruby/
+  def sieve(limit = 10000)
+    candidates = [nil, nil] + (2..limit).to_a
+    stop_at = Math.sqrt(limit).floor
+    candidates.each do |p|
+      # jump over nils
+      next unless p
+      # stop if we're too high already
+      break if p > stop_at
+      # remove all multiples of this number
+      (p*p).step(limit, p){ |m| candidates[m] = nil}
+    end
+    #remove unwanted nils
+    candidates.compact
+  end
+  
+  def include?(n)
+    while n >= @primes.max
+      add_next_prime!
+    end
+    @primes.include?(n)
+  end
+
+end
+