This is really crazy, does the book contain a prove for this?
How many pages are needed for the prove?
Or is it a trick such that there are only a few combinations can result
in a positive (and then prime) number?
Greetings, Markus
R.E. Boss schrieb:
Perhaps not similar but also remarkable is the following.
On page 200 in 'Music of the primes' by Marcus du Sautoy, there is the
formula (in classic mathematical notation)
(K+2)*
{1
- [WZ+H+J-Q]^2
- [(GK+2G+K+1)(H+J)+H-Z]^2
- [2N+P+Q+Z-E]^2
- [16(K+1)^3(K+2)(N+1)^2+1-F^2]^2
- [E^3(E+2)(A+1)^2+1-O2]^2
- [(A^2-1)Y^2+1-X^2]^2
- [16R^2Y^4(A^2-1)+1-U^2]^2
- [((A+U^2(U^2-A))^2-1)(N+4DY)^2+1-(X+CU)^2]^2
- [N+L+V-Y]^2
- [(A^2-1)L^2+1-M^2]^2
- [AI+K+1-L-I]^2
- [P+L(A-N-1)+B(2AN+2A-N^2-2N-2)-M]^2
- [Q+Y(A-P-1)+S(2AP+2A-P^2-2P-2)-X]^2
- [Z+PL(A-P)+T(2AP-P^2-1)-PM]^2
}
which produces a prime for every integer choice of A to Z, unless the
outcome is negative. Moreover, for every prime there is such a choice.
R.E. Boss
-----Oorspronkelijk bericht-----
Van: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] Namens John Randall
Verzonden: vrijdag 14 november 2008 18:24
Aan: Programming forum
Onderwerp: [Jprogramming] Minimal prime generators
At the opposite end of the spectrum from industrial strength methods
such as Miller-Rabin are generators which produce primes with minimal
(and apparently insufficient) resources.
Here are two of my favorites.
Rowlands' generator
This is a simple recurrence relation, starting with 7, whose first
differences are either 1 or prime.
f=:,{: + >:@# +. {:
d=:2 -~ /\ ]
1 -.~ d f^:1000 ] 7
5 3 11 3 23 3 47 3 5 3 101 3 7 11 3 13 233 3 467 3 5 3 941 3 7
Conway's Fourteen Fruitful Fractions
This is more mysterious. We take a list of fourteen magic fractions.
At each step we have an integer, starting with 2. We multiply the
integer by each of the fractions from left to right until we get
another integer. This is the next iterate. When an iterate is a
power of 2, the exponent is the next prime.
num=:17 78 19 23 29 77 95 77 1 11 13 15 15 55x
den=:91 85 51 38 33 29 23 19 17 13 11 14 2 1x
fff=:num%den NB. The fractions
h=:{.@:(#~ (=<.))@:(fff&*)
k=:(#~ (=<.))@:(2&^.)
k h^:(i.1e4) 2
1 2 3 5 7 11 13 17
Does anyone have any similar examples?
Best wishes,
John
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
