decompwlj 3D

Primes p such that p + 4 is prime and p == 9 (mod 10)

A074822 on the OEIS · family primes

Weight–level plate of Primes p such that p + 4 is prime and p == 9 (mod 10)
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 viewerA074822 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L57,941 · 57.94 %
Weight class, k ≤ L42,056 · 42.06 %
Ties, k = L30
On the level line L = 120,626
Forced level, l ≤ d²956
Range of a(n)19 … 64,904,629
Range of the jump d30 … 7,020
Largest weight k, level L64,897,759, 2,058,199

193 different gaps occur, from 30 to 7,020; the level share is 57.94 %; L = 1 holds 36 % of the level class.

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.