A328179 Number of distinct primes required to satisfy the Strong Goldbach Conjecture for all even numbers <= 2n.

0, 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17

Offset: 1

Author

Marcin Barylski, Oct 06 2019

Keywords

• nonn

Comments

The Strong Goldbach Conjecture asserts that all positive even integers >=4 can be expressed as the sum of two primes.

If the Strong Goldbach Conjecture is true, then a(n) > 0 for all n > 1 and a(n) <= a(n+1) for all n.

Examples

			a(1)=0 because 2 does not have any Goldbach partition.
a(2)=1 because 4=2+2 and 2 is the only prime required for all even numbers <= 4.
a(3)=2 because 4=2+2 and 6=3+3, thus 2 and 3 are required for expressing all even numbers <= 6.
a(7)=4 because using {2,3,5,7} it is possible to build all even numbers <= 14.
a(8)=5 because using either {2,3,5,7,11} or {2,3,5,7,13} it is possible to build all even numbers <= 16.
a(10)=5 because {2,3,5,7,13} are enough to build all even numbers <= 20.
		

Links

• Marcin Barylski, Comparison of A328179 with pi(n) for the first 10^4 numbers
• Marcin Barylski, Redundant Primes In Goldbach Partitions