Late 20^{th} century: Prime numbers are used to encrypt information over the Internet (e.g., online shopping).

2003: Every even number is the sum of two primes and at most eight powers of 2.

2013: (using computers) – every even number greater than 2 and smaller than can be expressed as the sum of two primes

2013: Proof of Goldbach’s weak conjecture – Every odd number greater than 5 can be expressed as the sum of three primes.

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