The year 2024 holds a few interesting mathematical properties.
Primarily, it is a leap year, necessitating the addition of an extra day – February 29. The earth takes approximately 365.2422 days to complete an orbit around the sun. Because our calendar year incorporates 365 days only, the 0.2422 of a day is not accounted for. Now 0.2422 is approximately 0.25, and 4 × 0.25 equals 1 day, so that's why we add an extra day every fourth year. However, this adds a little too many days, approximately 0.25 - 0.2422 = 0.0078 of a day per year. 0.0078 is approximately 0.01, or 1/100. This is why we must remove an extra year every 100 years despite 100 being divisible by 4. But once again, 0.01 - 0.0078 equals 0.0022, or 22/10000. In other words we removed too many days. We must add back 22 extra days over the span of 10,000 years. Adding one extra day every 400 years gets pretty close, and so that is what we do in practice. In summary, every number divisible by 4 is a leap year, unless it is also divisible by 100, but it remains a leap year if it is divisible by 400.
Next, let’s use 2024 to highlight a little-talked-about idea in maths. Did you know that 2024 is an Abundant number? Abundant numbers, by definition, are those whose proper divisors sum up to a value greater than the number itself. Proper divisors include all factors of the number except for the number itself. 2024 has proper divisors: 1, 2, 4, 8, 11, 22, 23, 44, 46, 88, 92, 184, 253, 506, 1012 which sum to 2296. Because 2296 > 2024, 2024 qualifies as an Abundant number. To put this in context, there are 9 abundant years in the 21st century: 2004, 2016, 2024, 2040, 2052, 2060, 2064, 2076, and 2088.
Additionally, 2024 qualifies as a Harshad Number, also known as a Niven number, denoting divisibility by the sum of its digits. In the case of 2024, the sum of its digits (2 + 0 + 2 + 4) equals 8, and 2024 is divisible by 8.
Another mathematical point is how 2024 contributes to confirming Goldbach's conjecture—a hypothesis asserting that every even integer greater than 2 can be expressed as the sum of two prime numbers. Notably, the prime numbers 2017 and 7 add up to equal 2024. Worth noting is that Goldbach’s conjecture has not yet been formally proven even though it has been tested for all even numbers up to four hundred trillion! An incredible feat in itself, but useless in proving that it is true for all numbers! Who knows, it may just be that the next even number can not be formed by the sum of two prime numbers (ad infinitum)!
In summary, 2024 is a Harshad Abundant leap year, affirming Goldbach’s conjecture. Feel free to express this idea with friends, I'm sure they will love hearing about the mathematical abundance of 2024!
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