March 7th, 2018, 10:01 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 320 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: 1,780 Thanks: 482 
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: 7,236 Thanks: 2412 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. 

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generator, prime, productive 
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