My primes functions

A few primes functions

Here are a couple of programs for working with primes.  The first is not so useful - just returning a list of all primes up to the parameter passed.

The next one you pass a list of knownPrimes and a new upper bound and primes are added onto the list returning an expanded knownPrimes at the end

The final one opens a file, checks that there are no composite numbers included by sorting the list and then checking that none of the later numbers are composites divisible by the earlier numbers.  It also checks that the number of primes in the file is in the range that you would expect.

So, we are missing a function to actually write the new list of primes onto disk...


What I learnt
How to open a file on the disk and also a common way to read in line by line.  For each line in the file open up the line and then use the strip() method to take out end of line keys and similar out of the string before converting into an integer.


listOfPrimes(n) - primes from 2 to n


def listOfPrimes(n):
    """supply a number, Returns a list of all the prime numbers from 2 up to parameter n"""

    myPrimes = [2]
    print(myPrimes[0])
    isAPrime = None #define is a prime - probably not needed
    
    for i in range(3,n+1): #up to n+1 in order to include n in range
        for j in range(len(myPrimes)): 
            if i % myPrimes[j] == 0:
                isAPrime = False
                break
            else:
                isAPrime = True
        if(isAPrime):      
            myPrimes.append(i)
            print(myPrimes[j+1])
                         
    return myPrimes




boundedListOfPrimes(knownPrimes, n) - adds primes up to n to an existing list of primes

def boundedListOfPrimes(knownPrimes,n):
    """supply a list of known primes and an upper bound
    
    works out the primes between the highest of knownPrimes and the upper bound.
    
    appends the newly found primes to the list 
    
    in order to work the knownPrimes list must be complete from 2 onwards.  """
        
    if len(knownPrimes) == 0:
        knownPrimes[0] = 2 #special case of first time to ever work out list set first value as 2
    
    isAPrime = None #initial declaration of IsAPrime - start assuming isAPrime is true - i.e. numbers are all prime
    highestKnownPrime = knownPrimes[len(knownPrimes)-1] #pick last one in the list
    print("highest known prime",highestKnownPrime)
    
    
    for i in range(highestKnownPrime,n+1): #n+1start testing from one more than last no in known primes
        for j in range(len(knownPrimes)):
            if i % knownPrimes[j] == 0:
                isAPrime = False
                break
            else:
                isAPrime = True
        if(isAPrime):      
            knownPrimes.append(i)
            #print(j+1,knownPrimes[j+1])
                        
    return knownPrimes
    


checkPrimesFile(primesFileName) - opens a file of primes and carries out some checks, returns the file

def checkPrimesFile(primesFileName):
    """purpose is to return an int list of numbers in a file after doing some checks that there
    are no composite numbers in the file
    
    
    asks for hte name of a primes file then reads in a text file of prime numbers and puts into an array
    checks that all numbers in the file are primes by sorting it to the low to high and 
    then starting from the lowest testing the lowest against all the highest to make sure 
    nothing missing - then finally checks the theoretical distribution of primes against 
    the number.
    
    Function has to be passed a null string or a name of a file.  If it is a null string then
    the function will ask for the name
    
        """
    
    from math import log
    
    if primesFileName == "": 
        primesFileName = input("Type the name of the Primes file")
        print("Workign on ",primesFileName)
        
    primesFileData = open(primesFileName)
    myPrimes=[]
        
    for line in primesFileData:
        myPrimes.append(int(str(line).strip())) #make sure an integer and the last number is stripped
        
    primesFileData.close()
    
    myPrimes.sort() #make sure that the lowest number is first
    includesAComposite = False #assume that file is valid to start with
    
    for i in range(0,len(myPrimes)): #for every prime in the list
        for j in range (i + 1,len(myPrimes)): #after sortign the list go through numbers bigger than i
            if myPrimes[j] % myPrimes[i] == 0:
                print ("found a composite number divisible by primes in the list - indedx is",j," number is", myPrimes[j])
                includesAComposite = True #as we found one
                break
            
    if includesAComposite:
        print("includes a composite or a duplicate prime so prime frequency data not checked")
    else:
        highestPrime = max(myPrimes)
        lowerBound = highestPrime / log(highestPrime)
        upperBound = lowerBound * 1.25506
        if (len(myPrimes) > lowerBound and len(myPrimes) < upperBound):
            print ("the number of primes " + str(len(myPrimes)) + " is within the bounds of ", lowerBound, upperBound)
        else:
            print ("out of bounds", len(myPrimes), lowerBound, upperBound)
        
    
           
    return myPrimes