Similar Questions
One can pose similar questions when primes are replaced by other special sets of numbers, such as the squares.
- It was proven by Lagrange that every positive integer is the sum of four squares. See Waring's problem and the related Waring–Goldbach problem on sums of powers of primes.
- Hardy and Littlewood listed as their Conjecture I: "Every large odd number (n > 5) is the sum of a prime and the double of a prime." Mathematics Magazine, 66.1 (1993): 45-47. This conjecture is known as Lemoine's conjecture (also called Levy's conjecture).
- The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, and proved by Melfi in 1996: every even number is a sum of two practical numbers.
Read more about this topic: Goldbach's Conjecture
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