Problem 92. Multiple covering sets for Sierpinski and for Riesel integers.

On April 2, 2025, Emilia Gurisatti sent the following interesting problem.

She is "estudiante de segundo año de la Licenciatura en Ciencias Matemáticas en la Universidad de Buenos Aires, Argentina"

Emilia found several (27) Sierpinski integers with 3 distinct covering sets. Emilia got the same kind of results for other several (23) Riesel integers.

Her results are published, since Mar 23, 2026, in:

https://oeis.org/A394518 & https://github.com/emiguri/A394518/blob/main/b394518.txt

and

https://oeis.org/A394519 & https://github.com/emiguri/A394519/blob/main/b394519.txt

On top of that she got two more results not already published but sent to me by mail on April 2, 2026.

Sierpinski integer with 4 covering sets, distinct:

218164505156603
Covering sets: {3,5,7,13,19,37,73}, {3,5,7,13,17,241}, {3,5,7,13,19,37,109} y {3,5,7,13,97,241,257}

Riesel integer with 4 covering sets, distinct:

16107442173648029
Covering sets  {3,5,7,13,19,37,73}, {3,5,7,13,17,241}, {3,5,7,13,19,37,109} y {3,5,7,13,97,241,257}

Wilfred Keller, who was also contacted and consulted during the development of Emilia's work, sent the following comment:

"The study of multiple covering sets presented by Emilia Gurisatti took me  by surprise. Long ago, I had encountered two "double" coverings, but had considered them as an annoying anomaly. They are contained in an unpublished draft of 1993. I didn't expect a systematic investigation of them..."

Emilia also make me notice that Arkadiusz Wesolowski, in 2015-2018 produced two covering sets for each one of 24 Serpinski integers (A263391) and also two covering sets for each one of 24 Riesel integers (A263392).

Here are the Covering sets found by Wesoloski for these 48 integers, and sent by him specially for this publication.

Emilia question is:

Q1. Can you find Sierpinski or Riesel integers with more than 4 covering sets?

My (CR) questions are the following ones:

Q2. Can you find Brier integers with 2 or more covering sets?

Q3. Can you give your opinion about the importance/significance of investigating and producing múltiple covering sets for individual S/R/B numbers?