WLBOTT: Yesterday two Elders of WLBOTT celebrated their 41st wedding anniversary (to each other). Can you tell me some special properties for the number 41?
Chat: Congratulations on the Elders’ 41st wedding anniversary! That’s a wonderful milestone. Here are some interesting properties and facts about the number 41:
**Prime Number**: 41 is a prime number, meaning it is only divisible by 1 and itself. It is the 13th prime number.
**Centered Square Number**: 41 is a centered square number, which means it can be represented as a square with a dot in the center and other dots around it forming concentric squares. The formula for the ( n )-th centered square number is ( n2 + (n-1)2 ). For ( n = 5 ), the result is 41.
**Sum of Three Squares**: 41 can be expressed as the sum of three squares in multiple ways:
( 41 = 42 + 22 + 12 )
( 41 = 52 + 22 + 02 )
**Euler’s Lucky Number**: Euler discovered that the quadratic polynomial ( n2 + n + 41 ) produces prime numbers for ( n ) from 0 to 39. This sequence of primes is often referred to as Euler’s lucky numbers.
**Hexagonal Number**: 41 is a centered hexagonal number, which means it can be visualized as a hexagon with a central dot and layers of dots surrounding it in hexagonal patterns.
**Sum of First Six Prime Numbers**: The sum of the first six prime numbers (2, 3, 5, 7, 11, and 13) is 41.
These properties show that 41 is quite an interesting number with various mathematical and cultural significance. Happy anniversary again!
In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a given city block distance of the center dot on a regular square lattice. While centered square numbers, like figurate numbers in general, have few if any direct practical applications[1], they are sometimes studied in recreational mathematics for their elegant geometric and arithmetic properties.
[1] “few if any direct practical applications“; i.e. WLBOTT
Quadrinia
Quadrinia – The WLBOTT Goddess and Protectoress of the number 41 (XLI), square roots, prime numbers under 101, and hard drive archives.
Centrovia
Centrovia – The WLBOTT Goddess and Protectoress of Moderation, pickled herring, carbon sequestration, and hexagonals.
Closenufeous (Greek) / Approximodus (Roman)
Closenufeous (Greek) / Approximodus (Roman) – The WLBOTT Trickster God of Almost Primes, Approximations, Dollar Cost Averaging, and Just-in-Time Manufacturing.
Empress Decimalina Digitina
Decimalina Digitina is the fairy queen of rounding errors, and an angry queen is she.
