Late 20th 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.
To the MNS presentation* There are infinitely many primes
* Goldbach’s conjecture: Every even number (greater than 2) can be expressed as the sum of two primes.
* Support: Every known even number can be expressed as a sum of two primes.
* The fraction of even numbers smaller than N which cannot be expressed this way tends towards 0 when N→∞.
* Any even number can be written as the sum of not more than 6 primes.
To the MNS presentationNumber theory (MSC2010#97F60)
* Prime/Composite (natural) number
* Semiprime
Logic (MSC2010#97E30)
* Theorem
* Conjecture
* Proof
* Refutation
* Open problem
To the MNS presentation
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