Prime Sieve
Pick primes from a table of 2 to 100. Their multiples disappear, and in the end only primes remain.
Chosen: none yet
How to play
Tap a number in the table that you think is prime. Its multiples are crossed out. Working from the smallest number up works best. "Next prime" does one step for you, and "Auto" runs to the end. Once you have chosen the primes up to √100 = 10 (2, 3, 5 and 7), every number left is prime.
Learn more
This method is called the Sieve of Eratosthenes, named after an ancient Greek scholar. Every composite number (a number above 1 that is not prime) has a factor no larger than its own square root. So any composite up to 100 is divisible by a prime of at most 10, and sieving with the primes up to 10 is enough. There are 25 primes up to 100, and 78 up to 400.