Prime Numbers by Bit-Length — Why Prime Density Always Decays
Автор: Jonathan Kendall
Загружено: 2026-01-13
Просмотров: 107
Описание:
In this video, we group integers by bit-length (binary size) and examine how many primes appear in each group. These “bit buckets” grow exponentially, while prime counts grow more slowly — causing prime density to decay as numbers get larger.
We:
Group integers into binary buckets
Compute prime density per bucket
Visualize how density drops as bit-length increases
Compare the observed decay to the classic approximation
1/ln(n)
This perspective connects:
binary representation
exponential growth
prime number distribution
and why primes become rarer at larger scales
No advanced number theory required — just careful counting and visualization.
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