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 March 7th, 2018, 11:01 PM #1 Senior Member   Joined: May 2015 From: Arlington, VA Posts: 394 Thanks: 27 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, 11:34 PM #2 Senior Member   Joined: Aug 2012 Posts: 2,102 Thanks: 606 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. Thanks from Loren Last edited by Maschke; March 7th, 2018 at 11:52 PM.
 March 8th, 2018, 04:13 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,515 Thanks: 2515 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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