Problems & Puzzles: Puzzles

Puzzle 916. Follow-up to Puzzle 58

Jan van Delden sent the following puzzle:

In puzzle 58 we asked for a sequence of consecutive primes p, such that q=4p^2+1 is prime.

It seems a bit unfair that the last digit of these primes p must be in the set {3,7}.

The other digits in the set {1,9} want some attention as well. To honor their existence:

 

We ask for a sequence of primes p, such that q=6p^2+1 is prime.

 

The smallest solutions are:

 

k=1, p= 5 (Oops, thatís not in the set I promised..)
k=2, p= 3229,3251

k=3, p= 325349,325379,325411

 Q. Please extend this table.

 

 

Contribution came from Emmanuel Vantieghem

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Emmanuel wrote on March 16, 2018

k = 4 : {518261, 518291, 518299, 518311}
k = 5 : {24225169, 24225191, 24225199, 24225239, 24225241}

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