decompwlj 3D

Primes p such that p+4 and p+12 are also prime

A046137 on the OEIS · family primes

Weight–level plate of Primes p such that p+4 and p+12 are 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 viewerA046137 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L63,433 · 63.44 %
Weight class, k ≤ L36,562 · 36.56 %
Ties, k = L14
On the level line L = 115,510
Forced level, l ≤ d²3,856
Range of a(n)7 … 204,692,569
Range of the jump d12 … 22,950
Largest weight k, level L204,648,877, 15,352,735

1,400 different gaps occur, from 12 to 22,950; the level share is 63.44 %; 3.9 % of terms are forced level (l <= d^2).

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.