pjc

# We make array of prime numbers with modulus 0 as long as product_sum < n
 
def prime? n
  (2..(n-1)).each { |x| return false if n % x == 0 }
  true
end
 
n = 600_851_475_143
a = []
product_sum = 1

pjc

y = 0
(1..999).each { |x| y = y + x if (x % 3 == 0) || (x % 5 == 0) }
puts y

pjc

# Create Fibonnaci Array
a = [1,2]
upto = 4_000_000
while a[-2] + a[-1] < upto
  a << a[-2] + a[-1] 
end
 
# Create sum of even Fibonnaci numbers
sum = 0
a.each { |x| sum+= x if x.even? }

pjc

def palindrome? x
  y = x.to_s
  checks = y.length / 2
  y[0..(checks-1)] == y[-checks..-1].reverse
end
 
def divideable? x
  999.downto(100).each { |y| return true if x % y == 0 && (x / y).to_s.length == 3 }
  false
end

pjc

upto = 20
 
def prime? x
  (2..x-1).each { |y| return false if x % y == 0 }
  true
end
 
# For speed reasons we want to find max possible increment
def increment upto
  a = 1

pjc

def sum_of_squares upto
  a = 0
  (1..upto).each { |x| a += x**2 }
  a
end
 
def square_of_sum upto
  a = 0
  (1..upto).each { |x| a += x }
  a**2

pjc

def prime? x
  (2..x-1).each { |y| return false if x % y == 0 }
  true
end
 
x       = 10_001 # We look for 10 001st prime number
n       = 3 # Start at 3 so we can skip even numbers
counter = 1 # Counter at 1 because 2 is prime number
 
while true

pjc

# Ideone.com can't handle the full integer, our integer n is only the relevant line of the 1000 digit number.  
 
# n = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588

pjc

# Euclid's formula yields Pythagorean triples for integers m and n with m < n: 
# a = m**2 - n**2 ; b = 2*m*n ; c = m**2 + n**2

x = 1000

def euclids upto 
  result = []
  (2..upto).each do |m| # Start at 2 as 1 results nothing anyway
    (1...m).each do |n| # Euclid's formula only works for m > n
      result << [m**2 - n**2, 2*m*n, m**2 + n**2]

pjc

x = 2_000_000

def prime? x
  (2...x).each { |i| return false if x % i == 0 }
  true
end
 
def primes upto
  a = []
  (2..upto).each { |i| a << i if prime? i ; puts i }