What is a Primel?
Primel is a number puzzle in which you find a hidden five-digit prime number in six guesses, where every guess must itself be a five-digit prime and each digit is coloured green, yellow or grey exactly as letters are in a Wordle-style word game.
Also known as: prime number Wordle, prime guessing game.
How do you solve a Primel?
- 01
Start from the last digit
A five-digit prime cannot end in 0, 2, 4, 5, 6 or 8, so the final digit is always 1, 3, 7 or 9. That is a quarter of the search settled before you guess. Choose an opener that ends in one of those and use its other four digits to test the rest.
- 02
Open with five different digits
As with letters, a guess that repeats a digit asks the same question twice. Pick a known prime with five distinct digits that spread across the range, such as one containing a low digit, a middle digit and a high digit, so the first row eliminates as much as possible.
- 03
Keep a list of primes handy in your head
The hard part of Primel is not the deduction but finding a prime that fits the constraints. Numbers ending in 1, 3, 7 or 9 whose digit sum is not a multiple of 3 are the candidates; check divisibility by 3 by adding the digits before you type, and the game will refuse anything that is not prime.
- 04
Finish by checking small divisors
In the endgame you may have two or three candidate numbers. Rather than guessing at random, test each against 7, 11 and 13 mentally or on paper. The one that survives is the guess to play, and a candidate that fails is a row saved.
Common Primel mistakes
- Treating it as a pure digit game. The answer is prime, so many digit combinations that fit the colours are impossible, and ignoring primality wastes rows on numbers that could never be the answer.
- Wasting a guess on an even ending. The last digit of the answer is always 1, 3, 7 or 9, so a guess ending in anything else throws away a tile.
- Assuming digits are distinct. A prime can repeat a digit, such as 11113 or 77773, and the colours only mark a repeated digit as many times as the answer contains it.
- Typing before checking. The game refuses a non-prime guess and does not charge a row, but every refusal is time lost, and in the timed mode time is the score.
Where does Primel come from?
Primel appeared in early 2022, in the wave of games that took the five-tile, six-guess format of Wordle, which Josh Wardle had released in 2021, and swapped the dictionary for something else. Its swap was the primes: the set of five-digit prime numbers is fixed and finite, so a guess can be checked by arithmetic rather than by a word list.
This is the site's own implementation of that puzzle type. There are 8,363 five-digit primes, and unlike a word game the answer pool and the guess list are the same set, so anything you are allowed to type could be the answer. A guess with a leading zero is not accepted, because it would not be a five-digit number.
How many guesses do you get in Primel?
Six, with five tiles per row. Every guess must be a five-digit prime with no leading zero; the game checks primality before accepting a guess, so an invalid number is turned away rather than scored.
Is Primel free, and when is the new prime published?
Primel is free and needs no sign-up. A new prime is set every day at midnight UTC, and there is a timed mode in which you solve as many primes as you can before the clock stops. An account is only needed if you want to appear on the leaderboard. It plays on a phone as well as a desktop.