... Look at the finite fields F_(2^N) and F_(5^N). What are the orders, of the element p in the multiplicative groups of this field? Call these orders o5 and...
Hi, I was just wondering what the state of play was with looking for a (pseudo-)prime of the form 2^p+3 - what search limits have been reached, and have any...
... Hi Norman, ... That is an interesting conjecture - perhaps you should send it to the primes mailing list? What is your reasoning for it? Regards, Paul...
Paul, Just a couple of observations regarding primes of the form 2^p+3. First, there should be infinitely many primes of this form. When p is even, the result...
Hi Robert, ... I believe that we are only interested in p prime here. ... Careful... that sort of reasoning is wrong - you are saying that given an infinite...
... Let me correct that to say "for reasonably large p". __________________________________________________ Virus checked by MessageLabs Virus Control Centre....
... reached, and ... being done a ... results were ... http://groups.yahoo.com/group/primenumbers/message/1023 might contain some results for 2^p+3 Paul U....
Well, the OLEIS (A057736) only has 2, 3, 7, 67. But looking at http://groups.yahoo.com/group/primeform/message/1218 it appears that some searching was going...
... Wow, I solved this problem at a national maths contest when I was about 13 y.o. My solution was something like this (it actually works for every odd number...
Paul, I obviously misunderstood your equation; I read it as (2^p) + 3 where p=2,result 7; p=3, result 11, and so on. I stand by my earlier statements (let's...
Most days there is quite a lag between "send" and the actually posting of a message on the group board. Today, for what ever reason postings are very...
... [SNIP - see Paul J's reply] ... I wouldn't expect them to have the same distribution. 2^p+1, being a cyclotomic form, has restrictions on what its factors ...
Hi all ! One year ago i had found a fast PRP for primes 2^p+3. I get no comments. We must modify the Luca-Lehmer Test. S=14 For T=1 TO p-1 S=(S^2-2) mod 2^p+3 ...
Note, the result must be 14 or 194 ! In few seconds i found primes of form 2^n+3 with n=7,12,15,16,18,28,30,55,67,84,228,390,784,1110, 1704 best wishes Norman ...
... No, you got it right :-) ... See Sierpinski numbers for a well-known counterexample: 78557*2^n+1 contains an infinite number of elements which are (5 mod...
... They of course have their own divisibility criterea. But one unrelated to (a^n+b^n) forms. Their criteria are more similar to those behind the 'fixed k...
... Just 'Phil', no need for 'Mr.' :-) ... Nope, I mean the finite field with p^N elements, where in this case p=2 and p=5. The statement, seen a few posts...
... For an infinity of easy to show counter examples, look at this form: k#+p If p is a "fixed" prime > 3, then the expression will be +-1 mod(6), however, the...
I would comment, except for the site seems to have disappeared. http://algo.inria.fr/banderier/Seminar/Vardi/index.html ... i.e. we sum 1/p for p in ak+b, i.e....
AFAIK the largest PRP of form 2^n+3 is still the one found by me in July 2001:- 2^122550+3 It is the 19th largest known PRP, according to Henri Lifchitz's...
We hear a lot about n^2+1 containing a infinite number of primes. A similar function may well be: floor(n^(3/2))+/-k (and obviously 3/2 is a variable too) Does...
re: Why did Phil C. cross the road, etc. Primatosis -- that most dreaded of diseases, that is caused by the in-ability of the mind to give up thinking about...
... Believe me, if while sitting in a 90C sauna, as relaxed and limp as a human can be, you start weighing up various prime-hunting algorithms, then you've...
