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6 solutions
The sequence is a list of primes, and the next prime is 19.
The image demonstrates the sieve of Eratosthenes, where multiples of 2 (except 2 itself) are removed with a blue vertical line, multiples of 3 (except 3 itself) are removed with a orange horizontal line, multiples of 5 (except 5 itself) are removed with a green diagonal line and multiples of 7 (except 7 itself) are removed with a purple vertical line. This process continues for each prime that you come across.