20201127, 01:14  #1 
"Rashid Naimi"
Oct 2015
Remote to Here/There
1,979 Posts 
Largest Known Prime N such that ...
Hey all,
What is the largest known Prime N such that Not looking for a probablePrime here. I assume the only way to prove a such a number primes would be via TrialFactoring. Thanks for your time. Last fiddled with by Dr Sardonicus on 20201127 at 01:20 Reason: Attempt at gixnif optsy 
20201127, 02:43  #2 
Feb 2017
Nowhere
2^{6}×5×13 Posts 
I haven't checked that neither N1 nor N+1 are completely factored. Assuming neither is, I can give a floor.
I just looked for largest number proved prime by some method other than those using factorizations of N1 or N+1. And the first method I thought of was ECPP, implemented by Primo. According to Ellipsa > Primo Top20, N = Partition(1289844341) (40000 decimal digits) is the largest prime certified by Primo. 
20201127, 02:57  #3 
"Rashid Naimi"
Oct 2015
Remote to Here/There
1,979 Posts 
Thank you for that.
I think there is a good chance that I am not the only one who has never heard of a partition of a number before. If so: https://en.m.wikipedia.org/wiki/Part...(number_theory) Cool discovery Paul. Congrats. Last fiddled with by a1call on 20201127 at 02:58 
20201127, 03:29  #4  
Jun 2003
2·3^{2}·269 Posts 
Quote:
Looking at large N1 proofs in factordb (http://www.factordb.com/nmoverview.p...age=500&skip=0) without trivial 100% N1 factorization, I see 4469^39366+4469^19683+1 (143695 digits) 

20201127, 03:34  #5 
"Rashid Naimi"
Oct 2015
Remote to Here/There
11110111011_{2} Posts 
Yes, I forgot about that because I don't understand it.
Thanks for the refresher. 
20201127, 04:51  #6 
"Rashid Naimi"
Oct 2015
Remote to Here/There
1,979 Posts 
I assume there must be much lager ones recorded at Top5k.
But we can leave it at that. My primary objective was to find out alternative methods to N+/1 if any. I guess it is pretty much them and trialfactoring. ECPP is factoring regardless. Thank you for the insights. 
20201127, 05:57  #7  
Nov 2016
2^{2}·691 Posts 
Quote:
What is the largest number proven to be prime by N1 / N+1 / combined methods, but without trivial factorization (i.e. N1 / N+1 is not divisible by b^n with large n) (like the prime (791^18731)/790, its N1 only has algebra factorization, and not divisible by 791^n with large n)? Last fiddled with by sweety439 on 20201127 at 05:58 

20201127, 06:46  #8  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010000101001_{2} Posts 
Quote:
Also, 123447^{1048576}123447^{524288}+1 is prime! (5,338,805 decimal digits) Time : 187808.030 sec. 

20201127, 07:21  #9 
"Curtis"
Feb 2005
Riverside, CA
11FD_{16} Posts 

20201127, 11:45  #10 
Jun 2003
4842_{10} Posts 
Well, serves me right for not going to the primary source for primes

20201127, 11:47  #11 
Jun 2003
2·3^{2}·269 Posts 
In the context of "I heard Elliptic Curve and factoring is the only thing I know those are used for"
/Justaguess Last fiddled with by axn on 20201127 at 11:49 
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