Hi, Group & DAVID. Proth theorem extended: Let Q= k*2^n +1, where 'n' is a odd natural number >=3 and k<= 2^n +1 also odd. If for some 'a', a^((Q-1)/4) ==...
... +1 ... I've also noticed that 'k' doesn't need to be 'odd' for 'Q' to remain odd and also testable by this extension of Proth's theorem; just re- place 'k'...
Thanks for the efforts, Can you also do something similar namely create a proof for Wagstaff: formula = (2^n + 1) / 3 Dividing by 3 shouldn't make a proof...
Hi David, More serious is the question for a proof formula for (2^n + 1) / 3 Making a test that proves them would be cool. The new mersenne conjecture is of...
... I tend to agree. But your latest message would have been more pertinent if you had withdrawn (or justified) ... Have you tacitly withdrawn this claim? ...
... Jens kindly pointed me to http://www.research.att.com/~njas/sequences/A000978 with (2^986191+1)/3 from Vincent. Congrats to Vincent on this large PrP. ...
Sure and now you see the reason why it's "most interesting" to make solid the conjecture to a proof for Wagstaff :) Show me the proof :) Thanks, Vincent...
... My standing at http://primes.utm.edu/bios/top20.php?type=person&by=PrimesRank is predicated on the assumption that the primality of a large cyclotomic...
I have noticed that all factors of a cyclotomic number Phi(n,b) (that is the n-th cyclotomic polynomial computed in the point b) are either a divisor of n or...
... (2^986191+1)/3 296873 Vincent Diepeveen 06/2008 Wagstaff prime, (2^n + 1) / 3, Base 27-Strong PRP, thanks to those who wrote the software for making...
David, I am looking for an algorithm given two large values of a and b not necessarily prime.( but a combination of a and b is prime.) how would one attack the...
Any algorithm which uses other than factors of a particular number. ... -- mohan srinivasan 99451-88695 [Non-text portions of this message have been removed]...
... I gave an obvious small example. To generalize it, simply set y = a - 2 x = b + 20 then (a*x - b*y) is divisible by (10*y + x) as requested, since (a*x -...
... http://www.numbertheory.org/courses/MP473/lectures/lecture8/page4.html Of course there are better written proofs in the text-books, but this just happened...
... Sorry, Paul, my out-of-work Gremlins fled, taking their Pari-GP files with them :-) Perhaps a statement of your intent might now be in order? As I see it: ...
... Thanks for showing some interest. My testing is programmed in C for speed. ... Why indeed! With BPSW and any other known-to-me "1+2-selfridge" tests can be...
... My basic idea, apart from doubly strong kroneckers, is to avoid, for any divisor "d" of "n", using: [1,-1;1,0] (mod d); [1,+1;1,0] (mod d); [0,-Q;1,0] (mod...
... No-one knows. But a guideline is that Pinch's limit of 10^21, for counting Carmichaels, is way below that for the widely believed Erdos asymptotic...
Hello, David and other primeform-alothians (j/k). how do I use PFGW to find primes of the form Q= k*2^n +1 where 'k' has a range of 1 < k < 2^(2n) +1, by...
Thanks David. Gives me a clue. The way my algorithm goes--if its 10Y=than a<=9, if it is 100Y than a<=99, if it is 1000Y, than a<=999... Hope u get the gist.. ...
David, Thanks a ton! I have been able to generate a generic one for what I was looking for: Y=a-k x=B+(10^k1).k as a first step. Now I need to impose the...
aX^n+bX^n-1+.....f to be divisible by 10X+p where a,b,c,d,----f , p are given... to find X. Regards Mohan ex: x^5+x^4+9. x^3+x^2+4.x+3 to be divisible by...
Hi, I introduce the interesting expression 1/(x^(1/x)-1). This is the reciprocal of the difference of x-th root of x and 1. Experimenting with the expression...
... Note that the maximum point of x^(1/x)-1 happens at the same x value as the maximum point of x^(1/x). Take the natural log of x^(1/x), and you get...
Hi , Indeed, my first attempt was to take the derivative of y = x^(1/x) - 1 and set it to zero.I forgot something because I used the rule y = x^n dy/dx =...
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