decompwlj 3D

Greater of twin primes

A006512 on the OEIS · family primes

Weight–level plate of Greater of twin primes
Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.
Open in the 3-D viewerA006512 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L46,930 · 46.93 %
Weight class, k ≤ L53,068 · 53.07 %
Ties, k = L29
On the level line L = 117,537
Forced level, l ≤ d²185
Range of a(n)5 … 18,409,201
Range of the jump d2 … 2,190
Largest weight k, level L18,407,929, 2,617,951

Past 5, every term is 1 mod 6, so l = 1 (mod 6): squares are possible and 29 ties occur, where the lesser twins (l = 5 mod 6) have none. The level share, 46.93 %, is close to the lesser twins' 47.77 %.

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.