Problems & Puzzles: Puzzles

Puzzle 1175  A variation of A322743 Paolo Lava sent the following nice puzzle: A variation of A322743: "Least prime such that complementing one bit in its binary representation at a time produces exactly n prime". Here the first 11 values Number of primes: n Least prime which produces n different primes 0 127 1 2 2 7 3 19 4 43 5 1487 6 10987 7 44971 8 44029 9 349667 10 4982051 11 80170037 Q. Can we extend the list beyond n=11?

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From May 11 to 17, 2024, contributions came from Michael Branicky, Simon Cavegn, Giorgos Kalogeropoulos, JM Rebert, V.F. Izquierdo, Paul Cleary

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 Michael Branicky wrote:

n  Least prime which produces n different primes
 

12 948583117

13 4537572437

14 2733418411

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Simon Cavegn wrote:

12  948583117
13  4537572437
14  2733418411
15  732198386671
16  362081961221

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Giorgos Kalogeropoulos wrote:

Next 3 terms are:

a(12) = 948583117

a(13) = 4537572437

a(14) = 2733418411

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 JM Rebert wrote:

n  p

11 80170037 8-digit prime

12 948583117 9-digit prime

13 12606151339 11-digit prime

14 2733418411 10-digit prime

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V.F. Izquierdo wrote:

12,   948583117

13  4537572437

14, 2733418411

 

el 15 debe ser mayor del primo  47154160069.

 

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Paul Cleary wrote:

I found two more solutions

 

New primes for initial prime 948583117: {814365389,1015691981,940194509,952777421,
949631693,948058829,948648653,948599501,948581069,948584141,948583373,948583109}
Number of new primes: 12

New primes for initial prime 2733418411: {2196547499,3001853867,2699863979,2750195627,2725029803,2731321259,2733483947,
2733385643,2733410219,2733422507,2733417899,2733418283,2733418427,2733418409}
Number of new primes: 14
 

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