Username53

#Problem Set 1 - Problem 1
#Name: Username53
#Collaborators: None
#Time: 2 days

print "This program will find and display the 1000th prime"


n = 1000                                #Sets limit on program

counter = 1                             #Starts prime number counter at one (2 already counted)                          
prime = 3                               #First test number is 3                          
limit = n                               #Total is limit                       

while (counter < limit):                #Run only while the # of primes is less than limit            
    divisor = prime/2                   #Divisor is the prime num./2 (integer division gives original divisor value of 1)            
    while (divisor > 1):                
        if prime % divisor == 0:        #Tests if a number is prime
            prime += 2                  #If number is not prime, next odd number is selected     
            divisor = prime / 2         #Divisor is now set to next odd number/2     
        else: divisor -= 1              #Number is prime     
    counter += 1                        #Increasers counter by 1
    prime += 2                          #Selects next odd number
print prime - 2                         #Once 1000th prime is reached, it is printed
 
#Problem Set 1 - Problem 2
#Name: Username53
#Collaborators: None
#Time: 1 hour

print "This program will findthe sum of the logarithms of all the primes from 2 to some number n, and print out the sum of the logs of the primes, the number n, and the ratio of these two quantities."

import math                                                    #gets math tools
prime = 3
counter = 1                                                    #counter
limit = int (raw_input("Please Enter a Number"))               #Input total number of primes desired
sum_of_primes = math.log(2)                                    #Start with log of 2
while prime < limit:                                           #Run only while prime<limit
    divisor = 3                                                #Start with divisor of 3
    while (divisor < math.sqrt(prime) and prime%divisor <> 0): #This is done when divisor < sqrt (prime) and for primes
        divisor += 2                                           #Sets divisor to next
        if divisor > math.sqrt(prime):
            sum_of_primes = sum_of_primes + math.log(prime)    #Add log of prime to sum of the log of primes
    prime += 2                                                 #Sets prime to next odd integer
print sum_of_primes                                            #Prints sum of the log of primes
print prime                                                    #The prime number chosen
ratio = sum_of_primes / prime                                  #gets ration of sum to number chosen
print ratio                                                    #prints ratio
  

#Problem Set 0
#Name: Username53
#Collaborators: None
#Time: 5-10 Minutes


last = raw_input("Please enter last name: ")
first = raw_input("Please enter first name: ")
print first,last