With a spirit of expanding on my previous post about checking numbers for primality, here's a quick way to generate a sequence of prime numbers using streams:

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public static LongStream primeSequence(long max) {
    return LongStream.iterate(2, i -> i + 1)
            .filter(x -> isPrime(x))
            .limit(max);
}

The above returns a LongStream of prime numbers up to a specified max value. It uses my previous prime checker function isPrime.