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March 10, 20262 citationsOpen Access

Digit Transitions of Twin Primes in Bases 6, 12, 18, 30, and 10: An Experimental Study

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VCVictor Eduardo Morales Cordoba

Key Points

  • This analysis aims to explore the last digits of twin prime pairs in various bases and confirm predicted digit transitions.
  • Analyzed over 3.4 million twin prime pairs across bases 6, 12, 18, 30, and 10.
  • Examined the last digits focusing on coprimality to the base.
  • Compared frequencies of admissible transitions and their equidistribution.
  • Identified observed digit transitions match predictions based on coprimality.
  • Frequencies of transitions are nearly identical across bases, supporting equidistribution.
  • Counts for bases 10 and 30 were identical due to the Chinese Remainder Theorem.

Abstract

We analyze the last digits of more than 3.4 million twin prime pairs in bases 6, 12, 18, 30, and 10. The observed digit transitions coincide exactly with those predicted by the condition that both primes must be coprime to the base. Moreover, the frequencies of the admissible transitions are nearly identical, providing empirical support for the expected equidistribution of twin primes among valid residue classes. This experiment provides a simple numerical illustration of the modular structure underlying twin primes and highlights the role of wheel factorization in prime distributions. A key observation is that the counts for base 10 and base 30 are identical, a direct consequence of the Chinese Remainder Theorem.

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Cite This Study

Victor Eduardo Morales Cordoba (2026) studied this question.

synapsesocial.com/papers/69af95b470916d39fea4d7e6https://doi.org/10.5281/zenodo.18912775
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