Largest Known Prime N such that ...

[a1call]

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.

[VBCurtis]

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.

[a1call]

Originally Posted by Batalov

10⁴⁷⁴⁵⁰⁰ + 999 · 10²³⁷²⁴⁹ + 1 (a palindrome) has 50% factorization and is 474,501 decimal digits long.

Also,
123447^1048576-123447⁵²⁴²⁸⁸+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.

[a1call]

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

[Nick]

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