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2020-11-27, 11:47   #12
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

198110 Posts

Quote:
 Originally Posted by VBCurtis What sorts of primes do you prove by trial factoring? In what context do you mean "ECPP is factoring regardless"?

I assume you prove them prime by ruling out the existence of prime factors less than or equal to square root of N.
But please correct me if I am wrong.
I assume elliptic curve testing does the same thing but that's perhaps because I have no clue what it does.

Last fiddled with by a1call on 2020-11-27 at 11:48

2020-11-27, 15:52   #13
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

120316 Posts

Quote:
 Originally Posted by a1call I assume you prove them prime by ruling out the existence of prime factors less than or equal to square root of N.
I didn't ask for the procedure, I asked which primes you would use that slowest-possible procedure on, instead of something faster.

No, ECPP isn't a factoring algorithm. You could try wiki for a basic explanation, which may still be over your head but at least it'll show you it's not trial factoring.

2020-11-27, 22:45   #14
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

7×283 Posts

Quote:
 Originally Posted by Batalov 10474500 + 999 · 10237249 + 1 (a palindrome) has 50% factorization and is 474,501 decimal digits long. Also, 1234471048576-123447524288+1 is prime! (5,338,805 decimal digits) Time : 187808.030 sec.
Links to Batalov's relevant primes: Kudos.

https://primes.utm.edu/primes/page.php?id=123041

https://primes.utm.edu/primes/page.php?id=118775

I see N-1 in both notes.

2020-11-27, 22:52   #15
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

7·283 Posts

Quote:
 Originally Posted by VBCurtis I didn't ask for the procedure, I asked which primes you would use that slowest-possible procedure on, instead of something faster. No, ECPP isn't a factoring algorithm. You could try wiki for a basic explanation, which may still be over your head but at least it'll show you it's not trial factoring.
Well here is the link to wiki and yes it is written in a Klingon dialect with which I am not familiar.

I will spend some time to see if I can decipher the numeric example but don't hold your breath.

https://en.wikipedia.org/wiki/Elliptic_curve_primality

Last fiddled with by a1call on 2020-11-27 at 22:52

 2020-11-27, 23:06 #16 Nick     Dec 2012 The Netherlands 2·7·113 Posts There is a good introduction to the mathematics of elliptic curves (aimed at people who did not study mathematics itself at university): https://press.princeton.edu/books/ha...elliptic-tales

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