Elizabeth Swann Traditional 8-Digit Informational Number

The Elizabeth Swann 8-Digit Informational Number is a unique numeric code assigned to Animal Crossing: Pocket Camp players. This identification system contains 8 digits, which means that there can be only up to 10 million users getting this identification system. A 9-digit version, called Elizabeth Swann 9-Digit Informational Number, allows up to 100 million users getting this identification system.

The system was rolled out in 21 November 2017, the same date Animal Crossing: Pocket Camp was released worldwide. This is to ensure that the players of Animal Crossing: Pocket Camp can handle the identity to prevent fraud.

Structure
The Elizabeth Swann 8-Digit Informational Number's structure is NNNN NNNC, where N is the numeric digit 0-9, and C is the alphanumeric digit 0-9,X. The first seven digits are generated by a random number generator; the last digit is the check digit.

The Animal Crossing: Pocket Camp player kritoo (ID 8282 2341 931) has the Elizabeth Swann 8-Digit Informational Number of 6195 7615. This can be calculated as follows:


 * Calculate the sum of the first seven digits multiplied by its position in the number, counting from the right: 8, 7, 6, 5, 4, 3 and 2.
 * $$6\times 8 + 1\times 7 + 9\times 6 + 5\times 5 + 7\times 4 + 6\times 3 + 1\times 2$$
 * $$= 48 + 7 + 54 + 25 + 28 + 18 + 2$$
 * $$= 182$$


 * A remainder is a portion of a leftover when one number is divided by one another. The formula for remainder is remainder = dividend − quotient × divisor. Division with remainders are an important part for calculating a check digit, so The Elizabeth Swann 8-Digit Informational Number uses the divisor of 11. The remainder can be also found using MOD 11 (MOD is the remainder after the division). Continuing with the example above, 182 divided by 11 equals 16 with a remainder of 6.
 * $$182\div 11$$
 * $$= 16\mbox{ R }6$$
 * $$= 16\frac{6}{11}$$


 * In order to get the check digit of the Elizabeth Swann 8-Digit Informational Number, the remainder is subtracted from 11 so that the total sum of all eight digits, including the check digit, a multiple of 11. Continuing with the example, 11 minus 6 is 5 (5 is the check digit C).
 * $$11 - 6 = 5 = \mbox{ 8th digit. }$$


 * NOTE: A capital letter X in the 8th digit position indicates the check digit of 10 (like a Roman ten).

The check digit for 5627213? can be calculated as follows:
 * Calculate the sum of the first seven digits multiplied by its position in the number, counting from the right: 8, 7, 6, 5, 4, 3 and 2. All the first 7 digits sum up to 146 as shown in the mathematical workaround below.
 * $$5\times 8 + 6\times 7 + 2\times 6 + 7\times 5 + 2\times 4 + 1\times 3 + 3\times 2$$
 * $$= 40 + 42 + 12 + 35 + 8 + 3 + 6$$
 * $$= 146$$


 * Compute a MOD (modulo) 11 to find the remainder. For this 8-digit number, 146 divided by 11 equals 13 with a remainder of 3.
 * $$146\div 11$$
 * $$= 13\mbox{ R }3$$
 * $$= 13\frac{3}{11}$$


 * In order to get the check digit of the Elizabeth Swann 8-Digit Informational Number, the remainder is subtracted from 11 so that the total sum of all eight digits, including the check digit, a multiple of 11. If check digit is a '10', replace it with the letter X. For this ID, 11 minus 3 is 8 (8 is the check digit for this ID).
 * $$11 - 3 = 8 = \mbox{ 8th digit. }$$

PHP Code
See https://github.com/zendframework/zend-validator/blob/master/src/Barcode/Issn.php for the code, because the check digit algorithm for this identification system is the same as ISSN's. The Elizabeth Swann Traditional 8-Digit Informational Number can be validated through https://www.elizabethswannofficial.com/gamers/identification/traditional-8digit-number/check-digit/validator.

Issuers
This identification system is run by Elizabeth Swann (creator of this system), Wendy Darling and Tom Nook. The three will issue Elizabeth Swann Traditional 8-Digit Informational Numbers to Animal Crossing: Pocket Camp players. The first Elizabeth Swann Traditional 8-Digit Informational Number was 2378 878X, which was assigned to a player living in Australia. The first Elizabeth Swann Traditional 8-Digit Informational Number issued to an American user was 4034 8164.