37, the median value for the second prime factor of an integer (grossack.site)

Article summary

The article discusses a mathematical fact that 37 is the median value for the second prime factor of an integer, meaning that roughly half of all numbers have a second prime factor less than or equal to 37. This fact is proven using the ideas from the Sieve of Eratosthenes and a paper by De Koninck and Tenenbaum. The author also explores the concept of the median kth prime and how it relates to the distribution of prime factors. The article concludes with some interesting exercises and open questions related to the topic.

Main themes

• prime factors
• median values
• interesting numbers
• number theory
• philosophy of mathematics
• set theory
• semiotics
• paradoxes and contradictions

What commenters say

• The concept of a median second prime factor is interesting and counterintuitive, but ultimately makes sense when considering the distribution of prime factors.
• The idea of interestingness in numbers is subjective and can lead to paradoxes and contradictions.
• Some numbers, such as 120, can be considered particularly interesting due to their unique properties and high number of divisors.
• The concept of zero and one as fundamental numbers is still a topic of debate, with some arguing that they are equivalent and others seeing them as distinct.
• The search for the most interesting number is a futile effort, as any number that is deemed interesting will become even more interesting due to its newfound status.
• The discussion of interesting numbers is more akin to a philosophical or semiotic debate than a mathematical one.
• The use of set theory as a foundation for modern mathematics implies that the empty set, similar to zero, is a fundamental concept.
• The debate over the nature of zero and one is a longstanding one, with roots in ancient philosophy and mathematics.