20211022, 15:57  #287 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,787 Posts 

20211022, 17:44  #288 
Aug 2020
79*6581e4;3*2539e3
13·31 Posts 
New Primorial Prime found
Recently a new 1 type primorial prime was found at PRPNet.
3267113#  1 It has 1418398 digits, making it the largest known one. The last 1 primorial prime was found more than 9 years ago, so this is quite the finding. The last +1 primorial prime hit is from 2001 btw. 20 years ago. :D I think it's an interesting type of prime due to its involvement in Euclid's proof of the infinitude of primes. Not many people seem to hunt for them though and they seem somewhat scarce taking into account that N+1 has lots of factors. MODERATOR NOTE: Moved to this thread, which already has this post and several followups related to this number. Last fiddled with by Dr Sardonicus on 20211023 at 02:37 
20211022, 18:03  #289  
Sep 2002
Database er0rr
3876_{10} Posts 
Quote:
The rarity of these numbers might put the next beyond the powers of BatalovPropper. MODERATOR NOTE: Moved to this thread, which already has this post and several followups related to this number. Last fiddled with by Dr Sardonicus on 20211023 at 02:38 

20211025, 17:34  #290  
Aug 2020
79*6581e4;3*2539e3
13×31 Posts 
Thanks for moving the post.
Quote:
I always forget the estimate for the digit size of primorials but the FFT size remains very managable even up to 20,000,000# where it's 3M. So if anyone was willing to put some larger ressources towards primorials or factorials, I'm pretty sure it'll yield some nice results before ending up in GIMPS waters. 

20211025, 20:53  #291  
Feb 2017
Nowhere
3^{2}·557 Posts 
Quote:
? 3267113/log(10) %1 = 1418889.1476543787883927627556683863802 As indicated above, 3267113#  1 actually has 1418398 digits. The estimate is a consequence of the Prime Number Theorem, which gives the asymptotic estimate ln(p_{k}#) = ln(2) + ln(3) + ... + ln(p_{k}) ~ p_{k} 

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