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March 7th, 2018, 11:01 PM   #1
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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?
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March 7th, 2018, 11:34 PM   #2
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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.
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Last edited by Maschke; March 7th, 2018 at 11:52 PM.
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March 8th, 2018, 04:13 AM   #3
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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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