Hidden Connections

In a separate blog of mine, I was writing about the introduction of a Central Bank Digital Currency or CBDC as it's most conveniently referred to. Whenever I see letters, I also see numbers. Such is my affliction. The numbers I see lie behind the letters when they are viewed as placeholders for numbers in non-decimal bases. In the case of CBDC, the obvious number base to consider is hexadecimal, base 16.

Bases of 14 and 15 are possible but they are not commonly used whereas hexadecimal is ubiquitous. So what decimal number does a hexadecimal CBDC convert to then. The answer is 52188. What are the hidden connections I refer to? Well, the connection lies in its factorisation which is \( 2^2 \times 3 \times 4349 \).

The connection is only apparent to me because I'm born on April 3rd 1949 which can be written as 4-3-49 in date notation and compressed to 4349. The smaller initial factors \(2^2=4\) and \(3\) reinforce this. I'm not suggesting any deep connection between myself and CBDC.  I'm just pointing this out as a mathematical curiosity. 

It's interesting to me to be able to see numbers lurking behind words and letters. See my recent post: Elements, Letters and Numbers. I also find it interesting to see dates as numbers and numbers as dates. See my recent posts: The Julian Day Number, Special Numbers, Special Dates, Turning Dates Into Numbers.

Getting back to my birthdate and birthdates in general, it can be observed that birthdates or any dates can be interpreted as numbers in the following ways using my birthdate as the example:

• DD - MM - YY with leading zeros and intermediate zeros optionally omitted.
  
  For example, 03 - 04 - 49 --> 30449 or, as it's said, "third of the fourth forty nine" (3449)
  
  
• MM - DD - YY with leading zeros omitted and intermediate zeros optionally omitted.
  
  For example, 04 - 03 - 49 --> 40349 or, as it's said, "fourth of the third forty nine" (4349)
  
  
• DD - MM - YYYY
  
  For example, 03041949 --> 3041949 or, as it's said, "third of the fourth nineteen forty nine" (341949)
  
  
• MM - DD - YYYY
  
  For example, 04 - 03 - 1949 --> 4031949 or, as it's said, "fourth of the third nineteen forty nine" (431949)
  
  
• YYYYMMDD
  
  For example, 19490403 and intermediate zeros are not usually dropped here. It's this format that I focused on in my blog titled Turning Dates into Numbers back in January of 2023.

Of these various representations, only three are prime:

3 - 4 - 49 = 3449 = 3449

3- 04 - 49 = 30449

4 - 3 - 49 = 4349

4 - 03 - 49 = 157 * 257

3 - 4 - 1949 = 3 * 113983

3 - 04 - 1949 = 3 * 43 * 23581

4 - 3 - 1949 = 3 * 7 * 67 * 307

4 - 03 - 1949 = 3 * 1343983

1949 - 04 - 03 = 3 * 167 * 38903