Mathematical analysis demonstrates the existence of twin primes between consecutive prime squares, suggesting a viable framework to verify the twin prime conjecture.
This paper started with specific prime factor analysis of natural numbers, then derived a new conjecture for proof by contradiction: At least one twin prime exists between the squares of consecutive primes. The statistical method was firstly adopted to verify the above conjecture. An innovative graphical method was also proposed to seek the mechanism of twin prime distributions to support the twin prime conjecture by contradiction.
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Hui Zhang (2026) studied this question.
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