20090817, 03:55  #1 
Oct 2007
2·17 Posts 
The Fischbach Prime a mersenne variation
Iv'e come up with a prime number generator that seems to generate
large primes, as far as I can test with a slightly greater effeciency than the mersenne equation can. Here's the equation (2^prime +1)/3= possibly prime Here's a side by side test between the Fischbach prime and the mersennne prime The mersenne prime is prime when 2 is raised to the following powers, 2,3,5,7,13,17,19,31,or 61. The Fischbach prime is prime when 2 is raised to the following powers,3,5,7,11,13,17,19,23,31,or 43. You people seem to be so clever on this forum why don't you come up with a system to test the Fischbach prime for primality and generate a prize winning prime and take the money to the bank. 
20090817, 04:26  #2  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
7·23·41 Posts 
Quote:
And that is significant because ... ? What about for n<=1million? What is the ratio? Is a "Fischbach prime" test more (or even as) efficient as a Mersenne prime test? If not and the test takes 10 times longer then can we expect a corresponding 10+ times increase in the number of primes found? Last fiddled with by retina on 20090817 at 04:34 Reason: than > then, stupid mistake. 

20090817, 04:34  #3 
Jun 2003
151C_{16} Posts 
Stop calling primes named after other people by your own name!

20090817, 04:39  #4 
Oct 2007
2×17 Posts 
The mersenne prime has shortcuts for testing primality I looked at my
equation for shortcuts for primality testing and couldn't find any, someone else may have some better luck, it's a lucrative proposition if you find them. 
20090817, 04:39  #5  
Dec 2008
341_{16} Posts 
Quote:
So I doubt anyone can come up with a primality test to prove the primality of Wagstaff ("Fischbach") primes that cuts the runtime by a polylogarithmic factor. Of course, a probable primality test may suffice. MillerRabin has a runtime of with a probability of error at most of 1/4 per iteration. Grantham's RQFT cuts this probability of error down to at most 1/7710 per iteration. Zhang's One Parameter Quadratic Base Test (a variant of the BPSW test) runs in about the same time (see his paper "A One Parameter QuadraticBase Version of the BailliePSW Probable Prime Test") and has a much less probability of error than RQFT. A TRIVIAL probable prime test which has a much lower probability of error than either RQFT and OPQBT that runs in time, where k=7 in the worst possible case, is by executing 1 iteration in RQFT followed by 1 iteration in OPQBT. I have attached a pdf file describing this RQFT+OPQBT test (I wrote it a couple months ago just for fun). It also talks more about Zhang's OPQBT in a bit more detail: Trivial_Probabilistic_Primality_Test.pdf P.S. I use the term "Selfridge" in this pdf, as it is a term coined and popularized by Jon Grantham which refers to the runtime of the MillerRabin test (in other words, ). Comments are more than welcome regarding the pdf file I attached. Last fiddled with by flouran on 20090817 at 05:30 

20090817, 04:58  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
7·23·41 Posts 
Aww, you guys all gave the game away so early.
I wanted Carl Fischbach to see if he could find the Wagstaff primes below 1million by himself, hence my question about the ratio for n<=1million. 
20090817, 05:20  #7 
Oct 2007
2·17 Posts 
I'm not making any claims beyond what Iv'e tested, the proof you want
is beyond my scope. 
20090817, 05:22  #8  
Dec 2008
7^{2}·17 Posts 
Quote:
Please look at my post; it is meant to be of help to you (I hope so at least): http://mersenneforum.org/showpost.ph...94&postcount=5 Kind Regards, flouran Last fiddled with by flouran on 20090817 at 05:26 

20090817, 05:43  #9 
Oct 2007
2·17 Posts 
Iv'e reinvented the wheel again, I was totally unfamiliar with the wagstaff
prime I'm half asleep here. 
20090817, 06:34  #10 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3^{2}·1,193 Posts 
Where is Dr. Bob when you need him?

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Sieving with powers of small primes in the Small Prime variation of the Quadratic Sieve  mickfrancis  Factoring  2  20160506 08:13 
Large Prime Variation of QS  Sam Kennedy  Factoring  9  20121218 17:30 
Integral Variation  flouran  Information & Answers  6  20090720 20:00 
Fischbach Representations.  Mr. P1  Puzzles  5  20071010 16:16 
Variation on a Martin Gardner puzzle  grandpascorpion  Puzzles  20  20070715 15:11 