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2⁹⁹⁹ + 1239 is the smallest 1000-bit prime. [Kulsha]

The first millennium with no prime is 13893290219204000 to 13893290219204999. [Grøndalen]

2⁹⁹⁹ + 33899096913 {+ 0,+ 2,+ 6,+ 8} is the first 1000-bit prime quadruplet. [Luhn]

1000 can be expressed using the first three primes as 2^3 * 5^3. [Priebel]

Here's a list of the first 1000 primes.

The 147th prime + 147 equals a thousand. [Bopardikar]