Amazon should've made Prime Day fall on a date corresponding to an actual three-digit prime number.
Amazon should've made Prime Day fall on a date corresponding to an actual three-digit prime number.
dd/mm/yyyy
1607 is prime
I maintain that dd/mm/yyyy and mm/dd/yyyy are stupid.
Big -> small is how we read numbers:
yyyy/mm/dd
For every day purposes, absolutely. For programming? Nope, the only right answer is big->small.
Honestly, the alternative to every day use is to stop using numbers for the month
12 is smaller than 31 is smaller than ∞, though.
Really, we can all come up with vastly reasonable reasons the date system we prefer makes the most sense… but in reality it’s all very subjective. Not only will different methods be appropriate for different situations… but some people just prefer their own way.
It’s all really moot, anyways. We should have been using stardates for the last 55 years anyways.
Actually, I disagree that DD/MM/YYYY even qualifies as being small to big.
If you actually treat it as a counter from 01/01/2024 onward, note that the first digit that moves is actually the second digit in the 8-digit representation. In terms of significance, the most significant digit is the 5th one in the string, then counting down the significance it’s 6th, then 7th, then 8th, then jumps back to the 3rd, then the 4th, then the 1st, then the 2nd.
I prefer the simple dy/my/dy/my format (with the year reversed for added ease of use). For example, today would be 14/02/70/72.
NIST and ISO have stopped responding to my emails, but I’m optimistic that the Türk Standardları Enstitüsü will eventually adopt it as their preferred standard.
ym/yd/md/yy. Also the year units are randomly swapped for encryption
July 16th is the 197th day of the year on non leap years. July 17th is the 199th day of the year on leap years.
Both of those are prime.
Well the convention was to store it as a 32 bit signed integer, so that is any number from -2^31 to (2^31 - 1). Prime numbers are formally defined as a subset of whole numbers, so let’s ignore the negative numbers and the number zero.
Fun fact: the largest signed 32-bit integer is itself a prime. And the wikipedia page lists it as the 105,097,565th prime.
By the time we hit the 2038 problem, there will have been about 105 million seconds since 1970 where the Unix time was a prime number. And it’s a 10-digit number in base 10, where prime frequency is something about 4% of the numbers.
Does that answer your question about prime frequency today? Eh, I’m sure someone else can figure that out. If not, I’ll probably have to wait until I’m in front of a computer.
If you’re looking for a proof:
Our base 10 system represents numbers by having little multipliers in front of each power of 10. So a number like 1234 is 1 x 10^3 + 2 x 10^2 + 3 x 10^1 + 4 x 10^0 .
Note that 10 is just (3 x 3) + 1. So for any 2 digit number, you’re looking at the first digit times (9 + 1), plus the second digit. Or:
(9 times the first digit) + (the first digit) + (the second digit).
Well we know that 9 times the first digit is definitely divisible by both 3 and 9. And we know that adding two divisible-by-n numbers is also divisible by n.
So we can ignore that first term (9 x first digit), and just look to whether first digit plus second digit is divisible. If it is, then you know that the original big number is divisible.
And when you extend this concept out to 3, 4, or more digit numbers, you see that it holds for every power of 10, and thus, every possible length of number. For both 9 and 3.
It works differently for each number. For 2, the last number has to be divisible by 2. For 3, the sum of the digits has to be divisible by 3 For 5, the number has to end with a 0 or a 5. For 7, it is kinda tricky. Take the last digit, double it, and subtract it from the numbers on the left. If the remainder is 0 or divisible by 7, the whole number is divisible by 7. For example 49: 9×2=18, 4-18=-14, -14/7=2 with remainder 0. For 700, 0×2=0, 70-0=70, 70/7=10 remainder 0.
This is usually specified for prime numbers, for non-prime number, you just do calculate the prime components of a number and combine the rules.
For example, divisibility by 15: it has to be divisible by 3 and 5. 1+5=6, 6/3=2 remainder 0. 15 ends with a 5. For number where with multiple same prime components the rules for these duplicate numbers have to apply multiple times. Like for 25, it has to end with a 5 or 0, and when dividing the number by 5, the result has to end with a 5 or a 0 aswell.