- #1
toddkuen
- 15
- 0
Take a prime[n] and double it, i.e., e.g., Pn (n=7) so prime[7] is 17, doubled to 34.
Take all unique arrangements of two primes from P2 (3) to P7 (17):
{3,3}, {3,5}, {5,5}, ..., {13, 17}, {17,17}
Add the pairs together, e.g., {3,3} = 3 + 3 = 6
Now eliminate duplicates, i.e., {5,5} and {3,7} both add up to 10, so just have one 10.
Then for 19 and 109 I find that all even numbers less than or equal to 19*2 and 109*2 respectively appear after you eliminate duplicates, i.e., all primes less than or equal to Pn generate all even numbers less than or equal to 2*Pn for 19 and 109.
Take all unique arrangements of two primes from P2 (3) to P7 (17):
{3,3}, {3,5}, {5,5}, ..., {13, 17}, {17,17}
Add the pairs together, e.g., {3,3} = 3 + 3 = 6
Now eliminate duplicates, i.e., {5,5} and {3,7} both add up to 10, so just have one 10.
Then for 19 and 109 I find that all even numbers less than or equal to 19*2 and 109*2 respectively appear after you eliminate duplicates, i.e., all primes less than or equal to Pn generate all even numbers less than or equal to 2*Pn for 19 and 109.