Prime Dates

How can we find all of the prime-number dates in a given year?

This is fairly simple in R. We’ll use the year 2017 as an example, and we’ll use American date order (ddmmyy). But the general approach can easily be adapted for other date formats.

First let’s find the prime-number dates for March 2017, in order to establish the basic method. To test whether a number is prime, we’ll use the isPrime() function from the numbers package.

Create the sequence 1 to 31 as characters. Paste ‘3’ to the beginning of each of these, and ‘17’ to the end (with no space in between), and then convert the resulting strings back to numeric, stored in the variable march.

Then use march as the argument to isPrime() and use that result as the index to march, which will return just those numbers in march that are prime.

library(numbers)
thirtyone <- as.character(1:31)
march <- as.numeric(paste(rep("3",31), thirtyone, rep("17",31), sep=""))
march[isPrime(march)]

[1]  3217  3517  3617  3917 31517 31817 32117 32717 32917

So there are 9 dates in March 2017 that are prime numbers.

The method can be easily extended to the entire year.

First, create vectors of day numbers (as characters) for the three possible lengths of month (31, 30, and 28). We can ignore leap years here because they are even numbers, and any date format that ends with the year will not have prime-number dates in even-numbered years. But it would not be difficult to adapt the code below for date formats like yyyymmdd and to add code for the case of February in leap years, which has 29 days.

thirtyone <- as.character(1:31)
thirty <- as.character(1:30)
twentyeight <- as.character(1:28)

Create a year variable, so that we can easily use this code for any odd-numbered year just by changing this variable, and set year to “17”.

year <- as.character(17)

Now create a for loop to cycle through each month (by number) and print out the prime-number dates for that month. We use the cat() function instead of print() in order to suppress the initial index numbers and to have better control over line breaks.

We’ll also keep a vector of all prime dates that we will count, sort, and print at the end.

allprimedates <- as.numeric(NULL)
for (n in 1:12)
{
  month <- as.character(n)
  if (n %in% c(1, 3, 5, 7, 8, 10, 12))
  {
    thismonth <- as.numeric(paste(rep(month, 31), thirtyone, rep(year, 31),sep=""))
  } 
  if (n %in% c(4, 6, 9, 11))
  {
    thismonth <- as.numeric(paste(rep(month, 30), thirty, rep(year, 30),sep=""))
  }
  else
  {
    thismonth <- as.numeric(paste(rep(month, 28), twentyeight, rep(year, 28),sep=""))
  }
  thismonthprimes <- thismonth[isPrime(thismonth)]
  cat(month.abb[n],"\n")
  cat(thismonthprimes,"\n")
  allprimedates <- c(allprimedates, thismonthprimes)
}

Jan 
1117 1217 11117 11317 11617 11717 12517 
Feb 
2417 2617 2917 21017 21317 21517 21617 21817 22717 22817 
Mar 
3217 3517 3617 3917 31517 31817 32117 32717 
Apr 
4217 4517 4817 41017 41117 41617 42017 
May 
5417 5717 51217 51517 51817 52517 52817 
Jun 
6217 6317 6917 61417 61717 62017 62417 62617 
Jul 
7417 7517 7717 7817 71317 71917 72617 72817 
Aug 
8117 8317 81017 81517 81817 82217 
Sep 
9817 92317 92717 
Oct 
101117 101917 102217 102317 
Nov 
11117 11317 11617 11717 111217 111317 113017 
Dec 
12517 12917 122117 

In all there are 78 prime-number dates in this year.

In numerical order they are:

 [1]   1117   1217   2417   2617   2917   3217   3517   3617   3917   4217   4517
[12]   4817   5417   5717   6217   6317   6917   7417   7517   7717   7817   8117
[23]   8317   9817  11117  11117  11317  11317  11617  11617  11717  11717  12517
[34]  12517  12917  21017  21317  21517  21617  21817  22717  22817  31517  31817
[45]  32117  32717  41017  41117  41617  42017  51217  51517  51817  52517  52817
[56]  61417  61717  62017  62417  62617  71317  71917  72617  72817  81017  81517
[67]  81817  82217  92317  92717 101117 101917 102217 102317 111217 111317 113017
[78] 122117