I gave an example earlier of attempting to find the factors of a number known to have two and only two prime factors. In this example I shall show how...
Hi all, Is there a program to sieve for 717*2^k-1?...... ... P.S.: Now, this is 99.98% off topic.....Are there any females in this group? Question was asked...
... NewPGen does sieving of "fixed k" for k*2^n-1 : http://www.utm.edu/research/primes/programs/NewPGen/ To get the full speed of LLR very small "k" are...
Hi, Actually you need to study the numbers around that area so that you can see that the division is anomalous to what you would expect to find. It's visually...
Hi: According to The Prime Glossary, a composite is a Carmichael number a^(n-1)==1 (mod n) for every a relatively prime to n. I ask: There's no bound to a in...
... Hash: SHA1 ... But by the Fermat-Euler Theorem: a^phi(n) == 1 (mod n) for any a != 0. Thus any a's lying in the same residue class modulo phi(n) are ...
Décio Luiz Gazzoni...
decio@...
Jul 1, 2004 11:58 pm
15069
Does anyone know if a number can be pseudoprime in more than one base? Specifically more than one prime base? Is there a proof or example either way? Kevin....
... (mod n) for every a relatively prime to n. Yes, the definition says the composite n is a Carmichael number iff: a^(n-1)==1 (mod n) for every a relatively...
... Yes. In particular, Carmichael numbers are pseudoprime to all bases < n that are relatively prime to n. If a number could be pseudoprime to at most one...
Yes, it can be. Specifically, the numbers I was talking about in my other email, the Carmichaels, are pseudoprimes for all bases a relatively prime to the...
OK, here's a bombproof way to factorize a Mersenne, given that the algorithm is implementable in a computer. Please make me aware of any counter-example should...
Taken another way p+1 divides n^p - 1. This isn't true. Harsh ... any ... a given ... memory ... given ... against ... 3^88 - 1. ... divide 2046, ... or 89. ...
Hi, Perhaps, I didn't put it the right way. Where p+1 is prime it divides n^p - 1 i.e. 11 divides 2^10-1 and 23 divides 2^22-1 More importantly, for my...
Perhaps it is K*p+1? Harsh ... the ... of ... number to ... computer ... in a ... n ... check it ... and ... 88+1 ... base ... divides ... The ... cases ... ...
Yes it should work! "Take a number known to be composite, in this case 2047 and check it against the smallest 3^n -1 number that it can divide." Finding n is...
Actually it is practical. Remember that you don't store the actual number, only the exponent. So in the example of 3^88-1 I know that everything below my...
See Crandall & Pomerance, Chapter 8. Specifically pp393/4 Paul...
Paul Leyland
pleyland@...
Jul 2, 2004 1:49 pm
15081
Hi: The order of a number n modulo p (with GCD(n,p)=1) is defined as the smallest exponent e such that n^e == 1 (mod p). Is there a straight way to find the...
... Yes, somewhat. The order of n mod p is in the set of the proper divisors of p-1. However, finding *which* of the proper divisors of p-1 is an order of n...
A week or so ago I posted a request for a volunteer to host the top-level ECMNET server which has to be moved from Microsoft Research in Cambridge, where it...
Paul Leyland
pleyland@...
Jul 5, 2004 9:21 am
15084
Can someone give me some more details on working out the order of an element mod p when we have a factorization of p-1? Please use the following example p =...
... an ... The best way I know is to start with N=p-1 and trial divide by each prime factor "q" of N. If 2^(N/q) = 1 mod p, then replace N by N/q and...
Hi, I have two experimental methods under investigation for this problem. One is the 'reverse algorithm' as mentioned a week or so back. A second method...
... base? ... bases < n ... that a ... simple. In fact, for the Fermat test, a number can be a pseudoprime to only finitely many different numbers of bases in...
Hello, I am very luky ! I juste find, with proth.exe, a "my be prime" of more than 800 000 digits ! I am verifing it... I have only scan for 0.5 prime in GFN...
Congratulations Daniel!! No wonder why I found nothing in my range, you got them all! :-) Jiong ... http://us.click.yahoo.com/L5YrjA/eSIIAA/yQLSAA/8HYolB/TM ...
