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PreprintarXiv licencearXiv

Parallel Searching Method for Verifying Finiteness of Prime Numbers Presented as Specific Linear Combinations of Factorials

  • Tomoki Mihara
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Abstract

As a new approach to search a counterexample of variants of Kurepa's conjecture, we investigate a parallel searching method of prime numbers p satisfying ∑k=0p−1 ck k! ≡ 0 pmodp for a given integer sequence (ck)k=0∞. As an application, we prove that there are only finitely may prime numbers of the form ∑k=0n (1+dk)! with (d,n) ∈ (ℕ≤ 25 ∖ {0,8,18,20,23,25}) × ℕ.

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Cite

BibTeXRIS
BibTeX
@misc{mihara2026parallel,
  title = {{Parallel Searching Method for Verifying Finiteness of Prime Numbers Presented as Specific Linear Combinations of Factorials}},
  author = {Tomoki Mihara},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28805},
  eprint = {2609.28805},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28805},
}
RIS
TY  - UNPB
TI  - Parallel Searching Method for Verifying Finiteness of Prime Numbers Presented as Specific Linear Combinations of Factorials
AU  - Tomoki Mihara
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28805
UR  - https://arxiv.org/abs/2609.28805
AB  - As a new approach to search a counterexample of variants of Kurepa's conjecture, we investigate a parallel searching method of prime numbers p satisfying ∑_k=0^p−1 c_k k! ≡ 0 pmodp for a given integer sequence (c_k)_k=0^∞. As an application, we prove that there are only finitely may prime numbers of the form ∑_k=0^n (1+dk)! with (d,n) ∈ (ℕ_≤ 25 ∖ {0,8,18,20,23,25}) × ℕ.
ER  -