mersenneforum.org PRP for F33?
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 2020-11-12, 06:00 #34 firejuggler     Apr 2010 Over the rainbow 256010 Posts Any factor of this would be the largest prime ever found.
 2020-11-12, 07:00 #35 VBCurtis     "Curtis" Feb 2005 Riverside, CA 13×367 Posts Why is that? Factors would have form 2kp+1, where p is 2^127-1, right? Last fiddled with by VBCurtis on 2020-11-12 at 07:00 Reason: k -> p
2020-11-12, 07:17   #36
LaurV
Romulan Interpreter

Jun 2011
Thailand

100100111000002 Posts

Quote:
 Originally Posted by VBCurtis Why is that? Factors would have form 2kp+1, where p is 2^127-1, right?
Yep, according with the current status of the search (k~~2^57) we can still find plenty of factors of ~185+ bits (around 55+ digits). Coarse calculus.

Last fiddled with by LaurV on 2020-11-12 at 07:22

 2020-11-12, 07:48 #37 firejuggler     Apr 2010 Over the rainbow 29×5 Posts My bad I made a mistake.
2020-11-12, 10:50   #38
Viliam Furik

"Viliam Furík"
Jul 2018
Martin, Slovakia

7048 Posts

Quote:
 Originally Posted by LaurV ...Coarse calculus.
I am not sure where is the calculus in this?

 2020-11-12, 12:29 #39 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 2,017 Posts See definitions other than 1b: https://www.merriam-webster.com/dictionary/calculus Last fiddled with by a1call on 2020-11-12 at 12:46
2020-11-12, 13:07   #40
Viliam Furik

"Viliam Furík"
Jul 2018
Martin, Slovakia

1C416 Posts

Quote:
 Originally Posted by a1call See definitions other than 1b: https://www.merriam-webster.com/dictionary/calculus
I don't accept these definitions to be valid.

Calculus is calculus, other mathematics is other mathematics.

2020-11-12, 13:14   #41
axn

Jun 2003

22×3×7×59 Posts

Quote:
 Originally Posted by Viliam Furik I don't accept these definitions to be valid. Calculus is calculus, other mathematics is other mathematics.
And English is English

2020-11-12, 14:19   #42
Dr Sardonicus

Feb 2017
Nowhere

2×7×17×19 Posts

Quote:
Originally Posted by LaurV
Quote:
 Originally Posted by Dr Sardonicus By the same "reasoning," all numbers larger than F33 also must be composite.
Aren't they? Show me a prime larger than F33...
Heck, I can't even "show you" F33. It has to be specified using accepted notation, so I will do the same to specify larger primes. Here are two:

1) The smallest prime exceeding F33; in Pari-GP notation, this could be expressed nextprime(2^(2^33)33 + 2) although Pari-GP only guarantees a value for which ispseudoprime() returns 1. Not a problem here.

Bertrand's Postulate (which has of course been proven) guarantees the existence of a prime between F33 and 2*F33.

2) The smallest prime factor of F2^(2^34) - 2.

2020-11-12, 14:57   #43
mathwiz

Mar 2019

157 Posts

Quote:
 Originally Posted by Dr Sardonicus Heck, I can't even "show you" F33. It has to be specified using accepted notation, so I will do the same to specify larger primes.
We can at least write F33 as 2^8589934592+1, yes? That may at least help to illustrate just how much larger it is than the largest-known prime, 2^82589933-1.

2020-11-12, 17:25   #44
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

9,547 Posts

Quote:
 Originally Posted by bbb120 you don't know Google and Wikipedia and Twitter and Facebook and YouTube can not be used in some country
Yahoo and Bing are available in China. I just tested that. The principle is the same. Search and search with various things like
"binary splitting" algorithm or "binary splitting" algorithm explained

Last fiddled with by Uncwilly on 2020-11-12 at 17:26

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