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Saturday, December 24, 2022

Easy Goldbach Bigger

 Consider again,


since the distance between two consecutive primes is roughly log(n) and the ratio of this distance to n is asymptotically zero by the Prime Number Theorem, the distance between the last prime and next prime as illustrated is also very narrow.  And by Bertrand–Chebyshev Theorem a prime exist between n and 2n.  We have,


the space below the last prime >n, is full of prime numbers.  So, as n, it is easier to find p+q=2n, although not necessarily certain.

The point is as n, Goldbach's Conjecture is easier to satisfy.