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June 18, 20260 citationsOpen Access

A Computational Study of Base-b Deletable Primes

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DODaniel Okwor

Key Points

  • This research explores the properties and counts of deletable primes in various bases, focusing on their growth patterns and underlying factors.
  • Systematic computation of n-digit base-b deletable primes for bases 3 to 12.
  • Analysis of growth ratios based on the parity of bases and mean offspring counts.
  • Proof of obstruction theorems regarding single-digit roots for deletable primes.
  • Deletable prime counts grow geometrically, with even bases growing approximately twice as fast as nearby odd bases.
  • The growth ratio is influenced by the phi function, resulting in distinct behaviors depending on base parity.
  • Two obstruction theorems identified, with counterexamples for moduli greater than 4.

Abstract

A prime is deletable in base b if its base-b digits can be removed one at a time, never creating a leading zero, so that every intermediate number is prime, ending at a single-digit prime. We carry out a systematic computation of the counts of n-digit base-b deletable primes for 3 = 5. Finally we record several new integer sequences. All code and verification records are public.

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Cite This Study

Daniel Okwor (2026) studied this question.

synapsesocial.com/papers/6a338e6e630953a74978f0f1https://doi.org/10.5281/zenodo.20710617
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