Verification of Sierpinski's Hypothesis H1
Published:Dec 27, 2025 00:01
•1 min read
•ArXiv
Analysis
This paper addresses Sierpinski's Hypothesis H1, a conjecture about the distribution of primes within square arrangements of consecutive integers. The significance lies in its connection to and strengthening of other prime number conjectures (Oppermann and Legendre). The paper's contribution is the verification of the hypothesis for a large range of values and the establishment of partial results for larger ranges, providing insights into prime number distribution.
Key Takeaways
- •Verifies Sierpinski's Hypothesis H1 for a significant range of values.
- •Establishes partial results for larger ranges, providing insights into prime distribution.
- •Uses prime gaps, pigeonhole principle, and Chebyshev function bounds in its analysis.
Reference
“The paper verifies Sierpinski's Hypothesis H1 for the first $n \leq 4,553,432,387$ and demonstrates partial results for larger n, such as at least one quarter of the rows containing a prime.”