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Obtains the total number of factors of p in n! for any prime p.

Python, 23 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```# Author: Samuel J Erickson # Date: 8/9/2013 # Description: de Polignac's formula gives all factors of p in n! for any prime # p. def polignac(num,p): """ input: num can be any positive integer and p and prime number. output: Gives the total number of factors of p in num! (num factorial). Stated another way, this function returns the total number of factors of p of all numbers between 1 and num; de Polignac's formula is pretty nifty if you are into working with prime numbers. """ factorsDict={} if num>1 and p==1: print("Invalid entry since 1 is the identity.") else: while num>1: factorsDict[num//p]=num//p num=num//p return sum(factorsDict) ```

#### 1 comment Samuel James Erickson (author) 9 years, 6 months ago

I forgot to mention that you will want to call getPLargest(num,p) in order to actually obtain the output from polignac's formula. Created by Samuel James Erickson on Fri, 9 Aug 2013 (MIT)