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 Twins, triplets and more (Posted on 2011-11-17)
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)

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 computer solution | Comment 1 of 5

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

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