Mertens Conjecture

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Cumulative sums of the Möbius mu function—which is essentially the parity of the number of factors in an integer, or zero if factors are repeated—follow an approximation to a random walk. The Mertens Conjecture from 1897 stated that this walk would always stay within But in 1985 it was proved that this is not so—although it is not known at what value of the first exception occurs.

Contributed by: Stephen Wolfram (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send