... An algorithm is a set of instructions that does rely on human intervention when it fails. A true theorem is one with no counterexamples. I think you need...
... Congratulations, Greg. This is a fine proof, combining state-of-the-art factorization with three types of primality testing and proving (BLS, CHG, ECPP). ...
... I admitted I did not write a clear algorithm - left out the most important findings of the theorem which I corrected ... Have you read the theory in the...
Hi, John Renze's PARI chg.gp script has just finished a test of 4955-digit number 4^8230-3 = 2^16460-2-1 (as some people prefer). It is the largest prime...
... It lives here: http://physics.open.ac.uk/~dbroadhu/cert/chgcertd.gp It checks the CHG part. To complete the proof you need to run BLS tests using pfgw -tc...
... Alas, your idea is not new - Damgard and Frandsen write the following in a paper soon to appear in the Journal of Cryptology: "Berrizbeitia and Berry[4]...
... When Boris Iskra, a co-author of Berrizbeitia, started posting his interesting primality proofs: http://primes.utm.edu/bios/page.php?id=484 Phil Carmody...
... Hi Paul, 2^64695-2^15-1 is a trinomial number. "My" numbers are b^n +/- (b-1). For b=2^k we have 2^(kn) +/- 2^k -/+ 1, so we meet here, if you consider...
... Yes, it is in "my" form. I'll include it in my tables (soon, maybe today). However, it illustrates a bit different approach: find a such base b that...
... It seems to me that the cases n=4,5,6,7 are also rather straightforward. For N = b^n-(b-1) they give 50%, 40%, 33.33%, 28.57% of N-1 whenever b and b-1 are...
Hi, ... Broadhurst primes? ... I'm rather interested in factorization for small b and large n. ... (-2^15)^4313 + 2^15 + 1 < 0 Are negative numbers primes? :-)...
... A non-zero integer N is prime iff a) N is a not a unit, u; b) every divisor of N is of the form u or N*u. In Z, there are merely two units: u=-1 and u=+1. ...
... One spot: http://primes.utm.edu/notes/faq/negative_primes.html The basic answer is that it is your choice. We often just ignore multiplication by units...
From: "Chris Caldwell" <caldwell@...> ... Pah! I must reciprocate by stating that the canonical primes are of course: {2} \/ { ... -11, -7, -3, 5, 13, ......
Wojciech: You mail is bouncing: < zireael.amu.edu.pl #5.0.0 X-Postfix; unknown user: "florek"> Please mail simply the factorfile that you used for pfgw -tc -h ...
... It is, indeed! Using only Wojtek's helpers for ... Primality testing 4^8230-3 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running...
I claim that N = 2^389335 + 2^97837 + 1 is prime. For this, I needed a single Pocklington test, with base=3. In less than an hour, OpenPFGW, running with the...
... Nice! Is your method applicable to 10^n-10^k-1? I suggest a PrimeForm group effort to look in the region n=150,000 and "k" in the region 25% and 25.2% of...
... I believe so. It's still a bit empirical as to how many master polynomials I shall need. But my old bold claims that the master polynomials can handle all...
... Because base 10 is a "special form" (NRD) in UTM's prime database. http://primes.utm.edu/top20/page.php?id=15 Jens, can you write a sieve? -- I have spare...
... Phil could probably also sieve much better than me. I have never made a discrete logarithm. A simple trial factor program could maybe reach 2^32. More than...
... I am willing to advise on its likely provability, as I did in my reply to Paul: http://groups.yahoo.com/group/primeform/message/7057 More generally, I...
... Phil's code for NRD is apperently not up to scratch either :-( So I'll stop pushing for a 150k NRD trinomial and leave it to others to suggest a project...
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