decompwlj 3D

Primes p such that p + 4 is also prime

A023200 on the OEIS · family primes · also known as Lesser of cousin primes

Weight–level plate of Primes p such that p + 4 is also prime
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 viewerA023200 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L46,766 · 46.77 %
Weight class, k ≤ L53,230 · 53.23 %
Ties, k = L31
On the level line L = 117,150
Forced level, l ≤ d²183
Range of a(n)3 … 18,466,729
Range of the jump d4 … 1,938
Largest weight k, level L18,464,569, 2,637,853

p with p + 4 prime. Past 3 every term is 1 mod 6, so l = 1 (mod 6) and ties can occur (31 here). The level share, 46.77 %, 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.