There is a huge (maybe infinite) number of twin primes, like (11,13), but only one triplet with d=2, i.e. (3,5,7).
However, one can get longer arithmetic series with other values of d.

Please list all the increasing arithmetic series such that:
a. They consist of at least 5 prime members.
b. Each number is under 100.

Example: 5,11,17,23,29. (d=6)

   10   ' limit to first 25 primes; 25th = 97
   15   Lim=25
   20   for Strt=1 to Lim-5
   30     for Fin=Strt+5 to Lim
   40       P1=prm(Strt):Pn=prm(Fin)
   50       Diff=Pn-P1
   60       for D=2 to int(Diff/4)
   70         if Diff/D=int(Diff/D) then
   80           :Good=1
   90           :for P=P1+D to Pn-D step D
  100             :if prmdiv(P)<>P then Good=0:endif
  110           :next P
  120           :if Good then
  130             :for P=P1 to Pn step D
  140                :print P;
  150             :next P
  160             :print tab(30);D
  170       next D
  180     next Fin
  190   next Strt

 

 series                        d
 5  11  17  23  29             6
 5  17  29  41  53             12

Posted by Charlie on 2011-11-17 12:37:18