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This research explores the properties and counts of deletable primes in various bases, focusing on their growth patterns and underlying factors.

June 18, 2026Open Access

A Computational Study of Base-b Deletable Primes

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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