March 7th, 2018, 10:01 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 374 Thanks: 26 Math Focus: Number theory  New prime generator?
In the spirit of Mersenne primes, does the product of the first n primes, minus one, generate other primes productively and efficiently?

March 7th, 2018, 10:34 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,999 Thanks: 572 
A primorial is the product of the first n primes. The sequence of primorials minus 1 that are primes is discussed here. The article doesn't say much. The sequence itself is OEIS sequence A006794. These are the primorial minus 1 primes. This doesn't answer your question as to whether prime production is productive or efficient, but it's a start. Last edited by Maschke; March 7th, 2018 at 10:52 PM. 
March 8th, 2018, 03:13 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,355 Thanks: 2469 Math Focus: Mainly analysis and algebra 
I imagine that it's very inefficient for large $n$ because of the need to find all the primes. Given an ordered list of primes, it might be reasonably efficient because there's no need to validate the result. 

Tags 
generator, prime, productive 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Linear generator  ungeheuer  Linear Algebra  0  June 16th, 2014 06:26 AM 
Primes map generator  Waflix  Computer Science  13  January 27th, 2014 05:43 PM 
Twin Prime Generator  chibeardan  New Users  7  May 26th, 2013 06:39 PM 
How to prove that 3 is a generator of Zp, p = 17?  asoracc  Abstract Algebra  2  February 27th, 2011 07:03 PM 
Combination generator  jhoffma4  Advanced Statistics  0  September 11th, 2009 06:22 PM 