Modul 49

Die Module

A Prime Number Shocker

A Prime Number Shocker

modulo 90

Extension 1

Extension 2

Continuation of Extension 1



 The preceeding table shows "by experiment":
•
c + + c -  = k-1   iff  k∈P
c + + c -  = k   iff  k = 2l, l∈N
c + + c -  < k-1   else
•
c - has local minima at all k such that 3|k,
λ + has local maxima at all k such that 3|k.
•
If
k and (k+1)/2 are prim and rest(k,12) = 1
then
c + (k) = c + (k+1) and c - (k) = c - (k+1).
 Find more interesting characteristics of c + , c - , c + + c -  and λ + .
 Find formula expressions or recurrence relations for c +  = f(k) and c -  = g(k).
 Proof all results.
 e.p. stoschek, d. schönfeld  29.07.2003
 stoschek@tcs.inf.tu-dresden.de, schoen@tcs.inf.tu-dresden.de

Extension 3

Continuation of Extension 2

Extension 4

Extension 5

Continuation of Extension 2

 Synopsis & generalization (at first) as a [.ps] file.
 e.p. stoschek, d. schönfeld  23.10.2003
 stoschek@tcs.inf.tu-dresden.de, schoen@tcs.inf.tu-dresden.de

Die Module