20230205, 20:41  #1 
Feb 2020
Germany
2^{3}×7 Posts 
Is there a form of primes similar to primorials but with the sum of primes?
I was just wondering if there is a named form of prime numbers which are generated by the formula k*sum(p)+/1?
With sum(p) I mean the sum of all primes up to p, in similar fashion to the primorials k*n#+/1? I did a google search and did not find an answer, maybe I used the wrong search parameters? Thanks in advance, hunson 
20230205, 20:56  #2  
"Rashid Naimi"
Oct 2015
Remote to Here/There
949_{16} Posts 
Quote:
With your proposed formula you get much smaller integers N with no easy way of factoring N+1 or N1. This would make them not very interesting for large provable primes. Just my 2 cents. Last fiddled with by a1call on 20230205 at 20:57 

20230205, 21:00  #3  
Jan 2021
California
3^{2}×61 Posts 
Quote:


20230205, 21:05  #4 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2,377 Posts 
These links might be useful:
https://en.wikipedia.org/wiki/Catego..._prime_numbers https://primes.utm.edu/glossary/page...83,(p)%3Dp%2B1. Last fiddled with by a1call on 20230205 at 21:08 
20230205, 21:46  #5 
If I May
"Chris Halsall"
Sep 2002
Barbados
3^{2}×5×251 Posts 

20230205, 22:00  #6  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2,377 Posts 
Quote:


20230205, 22:04  #7 
If I May
"Chris Halsall"
Sep 2002
Barbados
2C1F_{16} Posts 

20230207, 19:00  #8 
Feb 2020
Germany
2^{3}×7 Posts 
Thanks for all the (serious) answers ;)
@a1call: You are right, numbers of the form in question do not tent to grow very fast. They are most certainly not suitable for record primes and factoring is much more difficult. Thanks for the links, I will look into it. 
20230209, 16:47  #9  
Feb 2017
Nowhere
2^{4}·3·7·19 Posts 
Quote:
so will be of order n^{2}*log(n). Asymptotically, the sum divided by n^{2}*log(n) has limit 1/2 as n increases without bound, but for small n the ratio is somewhat larger. 

20230219, 07:24  #10 
Aug 2020
79*6581e4;3*2539e3
2·5·73 Posts 
What might be more interesting is factoring these numbers. You could even get rid of the +1 and just do the sum of primes.
https://oeis.org/A007504 is the respective sequence. 
20230219, 11:37  #11 
Feb 2020
Germany
111000_{2} Posts 
Asking as a non mathematician, what is the interesting outcome from factoring the sum of primes or the suggested primeform? What could be learned from that?

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