Prime Arithmetic Progression

Author

Eric W. Weisstein
July 25, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PrimeNumbers/PrimeArithmeticProgression.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PrimeArithmeticProgression.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

(Not Necessarily Consecutive) Primes in Arithmetic Progression

3

J. Sun, 2003

Do[
Print[{k,PrimeQ[405769059*2^180009-1+k*(45*2^368553-405769059*2^180009)]//Timing}],
{k,0,2}]

Do[
Print[{k,PrimeQ[405769059*2^180009-1+k*(45*2^368553-405769059*2^180009)]//Timing}],
{k,1,2}]

6

PrimeQ[Table[107+30k,{k,0,5}]]

Flatten[Position[PrimeQ[Range[107,107+30 5]],True]]-1

M. Oaks, Mar. 31, 2006

Length/@IntegerDigits/@Table[(27477652+3603821n)Primorial[3529]+1,{n,0,5}]

Do[Print[{n,PrimeQ[(27477652+3603821n)Primorial[3529]+1]//Timing}],{n,0,5}]

Ken Radenken, Apr 28, 2006

Length/@IntegerDigits/@Table[(32649185+3884057n)Primorial[3739]+1,{n,0,5}]

Do[Print[{n,PrimeQ[(32649185+3884057n)Primorial[3739]+1]//Timing}],{n,0,5}]

14

PrimeQ[Table[856378247603+30030k,{k,0,14}]]

16

PrimeQ[Table[(1723800454+529799k)Primorial[71]+1,{k,0,15}]]

PrimeQ[Table[(253456539 + 13892183k)Primorial[43]+1,{k,0,15}]]

22

PrimeQ[Table[11410337850553+4609098694200 k,{k,0,22}]]

Date: Sat, 19 Apr 2003 23:49:04 -0400
From: Markus Frind <flames@unforgettable.com>
To: NMBRTHRY@listserv.nodak.edu

PrimeQ[Table[376859931192959+18549279769020 k,{k,0,22}]]

23

Date: Sat, 24 Jul 2004 16:44:02 -0400
From: Markus Frind <flames@unforgettable.com>
To: NMBRTHRY@LISTSERV.NODAK.EDU
Subject: First AP23 Discovered

PrimeQ[Table[56211383760397+44546738095860k,{k,0,23}]]//Timing

Consecutive Primes in Arithmetic Progression

3

T. Alm, H. Rosenthal, J. K. Andersen, and R. Ballinger, 2003

Do[
Print[{k,TimeConstrained[PrimeQ[1205*2^16165-869+870*k],5 60]//Timing}],
{k,0,2}]

Position[Range@@(Function[k,1205*2^16165-869+870*k]/@{0,2}),_?PrimeQ]//Flatten//Timing

-Subtract@@@Partition[{1,871,1741},2,1]

6

PrimeQ[Table[121174811+30k,{k,0,5}]]

Flatten[Position[PrimeQ[Range[121174811,121174811+30 5]],True]]-1

a=1089533431247059310875780378922957732908036492993138195385213105561742150447308967213141717486151;

PrimeQ[Table[a+210 k,{k,0,6}]]

test[n_]:=Union[PrimeQ[Table[a+210 n+i,{i,1,209}]]]

Do[Print[i,". ",test[i]],{i,0,6}]

PrimeQ[Table[a+210 6+i,{i,1,209}]]