PRP for F33? - Page 4

firejuggler · 2020-11-12, 06:00

Any factor of this would be the largest prime ever found.

VBCurtis · 2020-11-12, 07:00

Why is that? Factors would have form 2kp+1, where p is 2^127-1, right?

LaurV · 2020-11-12, 07:17

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.

firejuggler · 2020-11-12, 07:48

My bad I made a mistake.

Viliam Furik · 2020-11-12, 10:50

Quote:

Originally Posted by LaurV

...Coarse calculus.

I am not sure where is the calculus in this?

a1call · 2020-11-12, 12:29

See definitions other than 1b:

https://www.merriam-webster.com/dictionary/calculus

Viliam Furik · 2020-11-12, 13:07

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.

axn · 2020-11-12, 13:14

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

Dr Sardonicus · 2020-11-12, 14:19

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 F_{2^(2^34) - 2}.

mathwiz · 2020-11-12, 14:57

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.

Uncwilly · 2020-11-12, 17:25

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

2020-11-12, 07:00	#35
VBCurtis "Curtis" Feb 2005 Riverside, CA 4605₁₀ 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, 12:29	#39
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 1,979 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, 06:00	#34
firejuggler Apr 2010 Over the rainbow 5×503 Posts	Any factor of this would be the largest prime ever found.

2020-11-12, 07:48	#37
firejuggler Apr 2010 Over the rainbow 2515₁₀ Posts	My bad I made a mistake.